Chapter 4.4, Problem 7E

To determine

To calculate: The derivative of y with respect to x .

Answer to Problem 7E

The derivative is $\frac{dy}{dx}=e^2-e^x$ .

Explanation of Solution

Given information: The equation of y in terms of x is given as,

  $y=x{e}^2-e^x$

Formula Used: $\frac{d\left(x^n\right)}{dx}=n\times x^{\left(n-1\right)}$

Calculation: Using the derivation,

  $\begin{array}{l}y=x{e}^2-e^x\\ \frac{dy}{dx}=\frac{d\left(x{e}^2-e^x\right)}{dx}\\ \frac{dy}{dx}=\frac{d\left(x{e}^2\right)}{dx}-\frac{d\left(e^x\right)}{dx}\\ \frac{dy}{dx}=e^2-e^x\end{array}$

So the derivative is $\frac{dy}{dx}=e^2-e^x$ .