Chapter 4, Problem 20RE

To determine

To Find: The derivative of the given function.

Answer to Problem 20RE

The derivative is $-8^{-t}\log 8$ .

Explanation of Solution

Given information: Given function $s=8^{-t}$

Formula used: $\frac{d(a^x)}{dx}=a^x\log a$ with chain rule.

Calculation:

  $\begin{array}{l}s=8^{-t}\\ \text{Differentiate}\text{with}\text{respect}\text{to}t\\ \frac{ds}{dt}=\frac{d(8^{-t})}{d(-t)}\times \frac{d(-t)}{dt}\\ \frac{ds}{dt}=8^{-t}\log 8\times -1\\ \frac{ds}{dt}=-8^{-t}\log 8\end{array}$