Chapter 4, Problem 1RE

To determine

To Find: The derivative of the given function.

Answer to Problem 1RE

The derivative is $3e^{3x-7}$ .

Explanation of Solution

Given information: Given function $y=e^{3x-7}$

Formula used: $\frac{d(e^x)}{dx}=e^x\text{and}\frac{d(x)}{dx}=1$ with chain and subtraction rule.

Calculation:

  $\begin{array}{l}y=e^{3x-7}\\ \text{Differentiate}\text{with}\text{respect}\text{to}x\\ \frac{dy}{dx}=\frac{d(e^{3x-7})}{d(3x-7)}\times \frac{d(3x-7)}{dx}\\ \frac{dy}{dx}=e^{3x-7}\times 3\\ \frac{dy}{dx}=3e^{3x-7}\end{array}$