Chapter 4.4, Problem 5E

To determine

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

Answer to Problem 5E

The derivative is $\frac{dy}{dx}=\frac{2}{3}\times e^{\left(\frac{2x}{3}\right)}$ .

Explanation of Solution

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

  $y=e^{\left(\frac{2x}{3}\right)}$

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

Calculation: Using the derivation,

  $\begin{array}{l}y=e^{\left(\frac{2x}{3}\right)}\\ \frac{dy}{dx}=\frac{d\left(e^{\left(\frac{2x}{3}\right)}\right)}{dx}\\ \frac{dy}{dx}=\frac{2}{3}\times e^{\left(\frac{2x}{3}\right)}\end{array}$

So the derivative is $\frac{dy}{dx}=\frac{2}{3}\times e^{\left(\frac{2x}{3}\right)}$ .