A quantity varies with according to

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

A quantity

y

varies with

x

according to

y = e^{\sin x}

, and

x

varies with time

t

x = t^{3}-t

. Determine

\dfrac{dy}{dt}

when

t = 1

Related theory

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

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