AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

y = e^{3\cos x}

. (a) Find

\displaystyle \frac{dy}{dx}

. (b) Determine all values of

x

in the interval

[0,2\pi]

for which

\displaystyle \frac{dy}{dx}=0

. (c) Classify each value obtained in part (b) as giving a local maximum or a local minimum of

y

on the given interval, giving reasons for your answer.

Related theory

Curve Analysis
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability
Differentiation Rules

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