Calculus 1 Exercises

263 videos • 38,208 views • by Wrath of Math A companion to my Calculus 1 playlist. It is ordered to follow the usual sequence of topics in a Calculus 1 course. This playlist contains videos on problems which are either too specific/short to go in the main playlist, or simply good for practicing the skills covered in the main course.
1
Classifying Essential Functions (Algebraic, Polynomial, Rational, etc. ...) | Calculus 1 Exercises
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2
Evaluate Limits from Graph | Calculus 1 Exercises
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3
Limit of x/(x^2-x) as x approaches 0 | Calculus 1 Exercises
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4
Limit of (x^2+x+6)/(x-2) by Factoring | Calculus 1 Exercises
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5
Limit of (x^2+x-6)/(x+3) as x approaches -3 | Calculus 1 Exercises
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6
Limit of (x^3-1)/(x-1) as x approaches 1 | Calculus 1 Exercises
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7
Limit of x^3+8/x+2 as x goes to -2 (by Factoring) | Calculus 1 Exercises
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8
Limit of (x^2-4)/(x^3-8) as x approaches 2 | Calculus 1 Exercises
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9
Limit of (sqrt(x+1)-1)/x as x goes to 0 | Calculus 1 Exercises
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10
Limit of (sqrt(2+x)-sqrtx)/x as x approaches 0 (Rationalize with Conjugate) | Calculus 1 Exercises
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11
Limit of (x-16)/(sqrt(x)-4) as x goes to 16 (Conjugate) | Calculus 1 Exercises
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12
Limit of (sqrt(x^2+9)-3)/x^2 as x approaches 0 (Using Conjugate) | Calculus 1 Exercises
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13
Finding Limits with Basic Limit Laws | Calculus 1 Exercises
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14
Limit of (1-e^x)/(1+2e^x) as x approaches Infinity | Calculus 1 Exercises
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15
Limit of (1-x)sin(1/(1-x)) as x approaches 1 | Calculus 1 Exercises
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16
Limit of sin(2x)/tanx as x Approaches 0 | Calculus 1 Exercises
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17
Limit of x*tan(1/x) as x approaches Infinity (no L'Hospital's Rule) | Calculus 1 Exercises
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18
Limit of sin(1/x) as x approaches 0 Does Not Exist | Calculus 1 Exercises
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19
Limit of x*sin(1/x) as x approaches Infinity | Calculus 1 Exercises
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20
Limit of sin(x)/x as x goes to Infinity (Squeeze Theorem) | Calculus 1 Exercises
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21
Limit of x^2*sin(1/x) as x Approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
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22
Limit of x^4*cos(2/x) as x Approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
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23
Master Trig Limits with sinx/x as x approaches 0 | Calculus 1 Exercises
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24
Trig Limits with sinx/x as x approaches 0 Master Problems | Calculus 1 Exercises
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25
Limit of tanx/x as x approaches 0 | Calculus 1 Exercises
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26
Limit of tan^2x/x as x approaches 0 (without L'Hospital's Rule!) | Calculus 1 Exercises
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27
Limit of sin(2x)/x as x approaches 0 | Calculus 1 Exercises
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28
Limit of sin(3x)/x as x approaches 0 | Calculus 1 Exercises
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29
Limit of sin(kx)/x as x approaches 0 | Calculus 1 Exercises
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30
Limit of sin^2(x)/x as x approaches 0 | Calculus 1 Exercises
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31
Limit of x*sin(1/x) as x approaches 0 | Calculus 1 Exercises
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32
Limit of x*sin(1/x^2) as x approaches 0 (Squeeze Theorem) | Calculus 1 Exercises
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33
Limit of sinx^2/x as x approaches 0 | Calculus 1 Exercises
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34
Limit of sinx/x^(1/3) as x approaches 0 | Calculus 1 Exercises
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35
Limit of sinx/(x+sinx) as x approaches 0 | Calculus 1 Exercises
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36
Limit of 2(1-cosx)/x as x approaches 0 | Calculus 1 Exercises
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37
Limit of (1-cos(x))/x^2 as x approaches 0 | Calculus 1 Exercises
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38
Limit of (1-cos8x)/2x as x approaches 0 | Calculus 1 Exercises
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39
Limit of (x+sinx)/(x+cosx) as x approaches Infinity | Calculus 1 Exercises
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40
Limit of sinxtanx/x as x approaches 0 | Calculus 1 Exercises
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41
Limit of cosxtanx/x as x approaches 0 | Calculus 1 Exercises
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42
Limit of arctanx as x approaches Infinity | Calculus 1 Exercises
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43
Limit of arctan(1/x) as x approaches 0 from the Right | Calculus 1 Exercises
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44
Limit of ln(sinx) as x approaches Pi from the Left | Calculus 1 Exercises
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45
Limits with Greatest Integer Function | Calculus 1 Exercises
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46
Continuity of the Greatest Integer Function | Calculus 1 Exercises
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47
Discontinuities with the Greatest Integer Function | Calculus 1 Exercises
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48
Intermediate Value Theorem to Find Roots | Calculus 1 Exercises
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49
Show e^(-x^2)=x has Solution with Intermediate Value Theorem | Calculus 1 Exercises
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50
Finding Horizontal Asymptotes of a Function Using Limits | Calculus 1 Exercises
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51
Find Horizontal Asymptotes with Conjugates | Calculus 1 Exercises
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52
Horizontal Asymptotes of (x^2-1)/(x^2+1) | Calculus 1 Exercises
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53
Derivative of x^2 by First Principles (limit definition) | Calculus 1 Exercises
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54
Derivative of 1/x by First Principles (limit definition) | Calculus 1 Exercises
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55
Derivative of x+1/x by First Principles (limit definition) | Calculus 1 Exercises
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56
Derivative of 1/x^2 by First Principles (limit definition) | Calculus 1 Exercises
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57
Derivative of sqrt(x) by First Principles (limit definition) | Calculus 1 Exercises
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58
Why tanx isn't Continuous on [0, pi/2] | Calculus 1 Exercises
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59
|x| is Continuous but not Differentiable | Calculus 1 Exercises
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60
The Only Power Rule Derivative Video You'll Ever Need | Calculus 1 Exercises
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61
Power Rule Master Problems | Calculus 1 Exercises
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62
Derivative of 1/x with Power Rule | Calculus 1 Exercises
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63
Second Derivative of 1/x | Calculus 1 Exercises
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64
Derivative of 1/x^2 with Power Rule | Calculus 1 Exercises
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65
Derivative of 1/x^3 | Calculus 1 Exercises
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66
Derivative of sqrt(x) with Power Rule | Calculus 1 Exercises
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67
Derivative of 1/sqrtx with Power Rule | Calculus 1 Exercises
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68
Derivative of sqrt(x)+1/sqrt(x) | Calculus 1 Exercises
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69
Find Equation of Line Tangent to x^(1/4) at (1,1) | Calculus 1 Exercises
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70
Derivative of Cube Root x | Calculus 1 Exercises
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71
Derivative of Cube Root x^2 | Calculus 1 Exercises
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72
Derivatives with Negative Exponents | Calculus 1 Exercises
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73
Derivatives with the Product Rule | Calculus 1 Exercises
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74
Product Rule Master Problems | Calculus 1 Exercises
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75
Derivative of sqrtx*(x-1) | Calculus 1 Exercises
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76
Derivative of sinxcosx with Product Rule | Calculus 1 Exercises
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77
Derivative of cos^2x with Product Rule | Calculus 1 Exercises
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78
Derivative of sinxtanx with Product Rule | Calculus 1 Exercises
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79
Derivative of sinxcosxtanx | Calculus 1 Exercises
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80
Derivative of xsecx with Product Rule | Calculus 1 Exercises
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81
Derivative of sqrt(x)*e^x with Product Rule | Calculus 1 Exercises
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82
Derivative of x^2e^xlnx (Product Rule with 3 Functions) | Calculus 1 Exercises
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83
Derivatives with the Quotient Rule | Calculus 1 Exercises
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84
Quotient Rule Master Problems | Calculus 1 Exercises
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85
Don't Use the Quotient Rule to Differentiate 1/x | Calculus 1 Exercises
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86
Derivative of x/(x-1)^2 | Calculus 1 Exercises
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87
Derivative of 1/sinx (Quotient Rule) | Calculus 1 Exercises
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88
Derivative of 1/cosx (Quotient Rule) | Calculus 1 Exercises
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89
Derivative of sec(x) with Quotient Rule | Calculus I Exercises
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90
Derivative of cotx (Quotient Rule) | Calculus 1 Exercises
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91
Derivative of sinx/x with Quotient Rule | Calculus 1 Exercises
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92
Derivative of sinx/x^2 with Quotient Rule | Calculus 1 Exercises
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93
Derivative of x/(1+cosx) | Calculus 1 Exercises
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94
Derivative of sinx/cosx with Quotient Rule | Calculus 1 Exercises
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95
Derivative of sinx/(1+cosx) with Quotient Rule | Calculus 1 Exercises
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96
Derivative of cotx/(1+cotx) with Quotient Rule | Calculus 1 Exercises
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97
Derivative of e^x/x with Quotient Rule | Calculus 1 Exercises
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98
Derivative of e^x/(1+x) with Quotient Rule | Calculus 1 Exercises
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99
Derivative of e^x/x^2 with Quotient Rule | Calculus 1 Exercises
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100
Derivative of sinx/e^x with Quotient Rule | Calculus 1 Exercises
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101
Derivative of (sinx+cosx)/(sinx-cosx) | Calculus 1 Exercises
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102
Derivatives with sinx and cosx Master Problems | Calculus 1 Exercises
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103
20 Chain Rule Problems but Each One Gets Harder | Calculus 1 Exercises
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104
Chain Rule Master Problems | Calculus 1 Exercises
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105
Derivative of sqrt(x+1) | Calculus 1 Exercises
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106
Derivative of 1/sqrt(x+2) | Calculus 1 Exercises
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107
Derivative of sqrt(1-x^2) with Chain Rule | Calculus 1 Exercises
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108
Derivative of sqrt(x^2+1) with Chain Rule | Calculus 1 Exercises
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109
Derivative of sqrt(x+sqrt(x)) with Chain Rule | Calculus 1 Exercises
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110
Derivative of (x + 1/x)^2 with Chain Rule | Calculus 1 Exercises
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111
Chain Rule with Radical Functions | Calculus 1 Exercises
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112
Derivative of sin(2x) with Chain Rule | Calculus 1 Exercises
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113
Derivative of sin(3x) with Chain Rule | Calculus 1 Exercises
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114
Derivative of sin(4x) with Chain Rule | Calculus 1 Exercises
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115
Derivative of sin(ax+b) | Calculus 1 Exercises
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116
Derivative of sin(x^2) with Chain Rule | Calculus 1 Exercises
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117
Derivative of sin^2(x) with Chain Rule! | Calculus 1 Exercises
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118
Derivative of sin(lnx) | Calculus 1 Exercises
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119
Derivative of sqrt(sinx) with Chain Rule | Calculus 1 Exercises
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120
How to Differentiate Any e^x with the Chain Rule | Calculus 1 Exercises
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121
Derivative of e^2x, e^x^2, e^sinx with Chain Rule | Calculus 1 Exercises
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122
Derivative of e^(-x) with Chain Rule | Calculus 1 Exercises
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123
Derivative of 1/e^x with Chain Rule | Calculus 1 Exercises
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124
Derivative of e^2x (Chain Rule) | Calculus 1 Exercises
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125
Derivative of e^3x (Chain Rule) | Calculus 1 Exercises
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126
Derivative of e^4x (Chain Rule) | Calculus 1 Exercises
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127
Derivative of e^(ax) with Chain Rule | Calculus 1 Exercises
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128
Derivative of e^x^2 (Chain Rule) | Calculus 1 Exercises
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129
Derivative of e^x^3 | Calculus 1 Exercises
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130
Derivative of e^sinx with Chain Rule | Calculus 1 Exercises
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131
Derivative of e^cosx with Chain Rule | Calculus 1 Exercises
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132
Derivative of e^tanx (Chain Rule) | Calculus 1 Exercises
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133
Derivative of e^(1/x) with Chain Rule | Calculus 1 Exercises
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134
Derivative of e^sqrt(x) with Chain Rule | Calculus 1 Exercises
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135
Derivative of e^e^x with Chain Rule | Calculus 1 Exercises
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136
Derivative of ln(2x) with Chain Rule | Calculus 1 Exercises
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137
Derivative of ln(3x) with Chain Rule | Calculus 1 Exercises
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138
Derivative of ln(x^2) without Chain Rule (and with) | Calculus 1 Exercises
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139
Derivative of ln(1/x) with Chain Rule | Calculus 1 Exercises
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140
Derivative of ln(lnx) with Chain Rule | Calculus 1 Exercises
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141
Derivative of ln(sinx) with Chain Rule | Calculus 1 Exercises
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142
Derivative of ln(secx) with Chain Rule | Calculus 1 Exercises
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143
Derivative of sqrt(lnx) with Chain Rule | Calculus 1 Exercises
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144
Derivative of ln|x| (a piecewise derivative) | Calculus 1 Exercises
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145
Derivative of sin(x^2), sin^2(x), and sin(2x) with Chain Rule | Calculus 1 Exercises
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146
Derivative of sin(x^3), sin^3(x), and sin(3x) with Chain Rule | Calculus 1 Exercises
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147
Derivative of sin^2(x), sin^2(2x), and sin^2(x^2) with Chain Rule | Calculus 1 Exercises
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148
Derivative of cos(2x) with Chain Rule | Calculus 1 Exercises
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149
Derivative of cos(ax+b) | Calculus 1 Exercises
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150
Derivative of cos(x^2) with Chain Rule | Calculus 1 Exercises
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151
Derivative of cos^2x with Chain Rule | Calculus 1 Exercises
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152
Derivative of cos(x^2), cos^2(x), and cos(2x) with Chain Rule | Calculus 1 Exercises
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153
Derivative of cos^2(3x) | Calculus 1 Exercises
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154
Derivative of tan(x^2), tan^2(x), and tan(2x) with Chain Rule | Calculus 1 Exercises
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155
Derivative of tan(x^2) with Chain Rule | Calculus 1 Exercises
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156
Derivative of tan^2(x) | Calculus 1 Exercises
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157
Derivative of tan^3(x) | Calculus 1 Exercises
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158
Derivative of sec(x) with Chain Rule (Secant Derivative) | Calculus 1 Exercises
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159
Derivative of sec^2(x) with Chain Rule | Calculus 1 Exercises
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160
Derivative of sec^3x (Chain Rule) | Calculus 1 Exercises
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161
Derivative of arctan(1/x) | Calculus 1 Exercises
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162
Second Derivative of sqrt(sinx) | Calculus 1 Exercises
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163
Second Derivative of sqrt(cosx) | Calculus 1 Exercises
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164
Limit of x*lnx as x approaches 0 (L'Hospital's Rule) | Calculus 1 Exercises
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165
Derivative of csc(x^2), csc^2(x), and csc(2x) with Chain Rule | Calculus 1 Exercises
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166
Limits with the Natural Log | Calculus 1 Exercises
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167
Limit of lnx/(x-1) as x approaches 1 (L'Hospital's Rule) | Calculus 1 Exercises
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168
Limit of lnx/(x-1) as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
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169
Limit of lnx/sqrtx as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
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170
Limit of lnx/x as x approaches 0 from Right | Calculus 1 Exercises
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171
Limit of (e^x-1)/x as x approaches 0 (L'Hospital's Rule) | Calculus 1 Exercises
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172
Limit of lnx/x as x goes to Infinity (L'Hospital's Rule) | Calculus 1 Exercises
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173
Limit of ln(lnx)/x as x approaches Infinity (L'Hospital's Rule) | Calculus 1 Exercises
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174
L'Hospital's Rule Twice! Limit of e^x / x^2 as x approaches Infinity | Calculus I Exercises
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175
Limit of (e^x-1-x)/x^2 with L'Hospital's Rule Twice! | Calculus 1 Exercises
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176
Limit of x^3*e^(-x^2) as x approaches Infinity with L'Hospital's Rule | Calculus 1 Exercises
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177
Limit of e^x/x^n as x goes to Infinity | Calculus 1 Exercises
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178
Limit of x^x as x approaches 0 | Calculus 1 Exercises
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179
How to Solve 1^Infinity Indeterminate Form Limits | Calculus 1 Exercises
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180
Limit of (1+x)^(1/x) as x goes to 0 (L'Hospital's Rule) | Calculus 1 Exercises
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181
Derivative of arcsin(x) with Implicit Differentiation | Calculus 1 Exercises
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182
Derivative of arcsin(x^2), arcsin^2(x), and arcsin(2x) with Chain Rule | Calculus 1 Exercises
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183
How to Find Derivatives of arcsin with Chain Rule | Calculus 1 Exercises
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184
Derivative of arccos(x) with Implicit Differentiation | Calculus 1 Exercises
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185
Derivative of arccos(x^2), arccos^2(x), and arccos(2x) with Chain Rule | Calculus 1 Exercises
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186
Derivative of arctanx | Calculus 1 Exercises
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187
How to take Derivatives of Absolute Value Functions | Calculus 1 Exercises
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188
Derivative of e^xy (Implicit Differentiation) | Calculus 1 Exercises
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189
Derivatives of log Functions with Any Base (and Chain Rule) | Calculus 1 Exercises
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190
Implicit Differentiation with Exponential Functions | Calculus 1 Exercises
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191
Second Derivative Implicitly | Calculus 1 Exercises
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192
2024 AP Calculus AB FRQ 5 Solution | Calculus 1 Exercises
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193
Derivative of x^(1/x) with Logarithmic Differentiation | Calculus 1 Exercises
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194
Derivative of x^x using Logarithmic Differentiation | Calculus 1 Exercises
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195
Find Derivative of x^sqrt(x) without Logarithmic Differentiation | Calculus 1 Exercises
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196
Derivative of (1+x)^x with Logarithmic Differentiation | Calculus 1 Exercises
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197
Derivative of x^e^x (Logarithmic Differentiation) | Calculus 1 Exercises
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198
Derivative of sin(x)^x (Logarithmic Differentiation) | Calculus 1 Exercises
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199
Derivative of 2^x | Calculus 1 Exercises
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200
Linearization of a Function at a Point is Easy! | Calculus 1 Exercises
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