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AP® Calculus AB-BC

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Compute Derivative of Generic Exponential Function

APCALC-DEG1G5

Let $H(t)=\frac{a}{t^{40}}-b \cdot e^t$ where $a$ and $b$ are both fixed constants.

What is $ H'(t) $?

A

$H'(t)=-\cfrac{41a}{t^{40}}-b \cdot t \cdot e^{t-1}$

B

$ H'(t)=-\cfrac{41a}{t^{42}}-b \cdot e^t$

C

$ H'(t)=-\cfrac{40a}{t^{39}}-b \cdot t \cdot e^{t-1}$

D

$ H'(t)=-\cfrac{40a}{t^{41}}-b \cdot e^t$