Chapter 4.2, Problem 32E

To determine

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

Answer to Problem 32E

  $\frac{dy}{dx}=-\frac{3}{5}\times x^{\left(-\frac{8}{5}\right)}$

Explanation of Solution

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

  $y=x^{\left(-\frac{3}{5}\right)}$

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

Calculation: Using the derivation,

  $\begin{array}{l}\frac{dy}{dx}=\frac{d\left(x^{\left(-\frac{3}{5}\right)}\right)}{dx}\\ \frac{dy}{dx}=-\frac{3}{5}\times x^{\left(-\frac{3}{5}-1\right)}\\ \frac{dy}{dx}=-\frac{3}{5}\times x^{\left(-\frac{8}{5}\right)}\end{array}$

So the derivative of y with respect to x is $\frac{dy}{dx}=-\frac{3}{5}\times x^{\left(-\frac{8}{5}\right)}$ .