Let where . Find when…

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

Problem

Let

y=(3x+2)^{4}

where

x=2t^{2}

. Find

\displaystyle \frac{dy}{dt}

when

t=1\,\text{s}

. (a)

12\,288

(b)

49\,152

(c)

24\,576

(d)

8\,192

Related theory

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

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