121616949-math.6 - 72 4.7 Derivatives of the exponential...

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vi Contents 3 Rules For Finding Derivatives 45 3.1 The Power Rule . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Linearity of the Derivative . . . . . . . . . . . . . . . . . . . . 48 3.3 The Product Rule . . . . . . . . . . . . . . . . . . . . . . . . 50 3.4 The Quotient Rule . . . . . . . . . . . . . . . . . . . . . . . . 53 3.5 The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Transcendental Functions 63 4.1 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . 63 4.2 The Derivative of sin x . . . . . . . . . . . . . . . . . . . . . . 66 4.3 A hard limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 The Derivative of sin x , continued . . . . . . . . . . . . . . . . . 70 4.5 Derivatives of the Trigonometric Functions . . . . . . . . . . . . 71 4.6 Exponential and Logarithmic functions
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Unformatted text preview: . . . . . . . . . . . . . 72 4.7 Derivatives of the exponential and logarithmic functions . . . . . 75 4.8 Limits revisited . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.9 Implicit Differentiation . . . . . . . . . . . . . . . . . . . . . . 84 4.10 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . 89 5 Curve Sketching 93 5.1 Maxima and Minima . . . . . . . . . . . . . . . . . . . . . . . 93 5.2 The first derivative test . . . . . . . . . . . . . . . . . . . . . . 97 5.3 The second derivative test . . . . . . . . . . . . . . . . . . . . 99 5.4 Concavity and inflection points . . . . . . . . . . . . . . . . . 100 5.5 Asymptotes and Other Things to Look For . . . . . . . . . . . 102...
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