Chapter 3.4, Problem 4E

To determine

To find : $dy/dx$ .

Answer to Problem 4E

  $\frac{dy}{dx}=-5e^{-5x}$

Explanation of Solution

Given information :

  $y=e^{-5x}$ .

Formula needed :

  $\frac{d}{dx}\left(e^{ax}\right)=e^{ax}\cdot \frac{d}{dx}\left(ax\right)$

Differentiate $y=e^{-5x}$ with respect to $x$ .

  $\begin{array}{c}\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left(e^{-5x}\right)\\ \frac{dy}{dx}=e^{-5x}\frac{d}{dx}\left(-5x\right)\\ \frac{dy}{dx}=-5e^{-5x}\end{array}$

Hence, $\frac{dy}{dx}=-5e^{-5x}$ .