Chapter 3, Problem 26RE

To determine

To find:The derivative of the given function.

Answer to Problem 26RE

The derivative function of $y=4x^2\left(x^{-1}+3x^{-4}\right)$ is $\frac{dy}{dx}=4-24x^{-3}$ .

Explanation of Solution

Given information: $y=2x^{-2}\left(x^5-x^3\right)$ .

Formula used:

• Derivative rule: $\left(x^n\right)\prime =n\left(x^{n-1}\right)$

Calculation:

  $\begin{array}{l}y=4x^2\left(x^{-1}+3x^{-4}\right)\\ y=4\left(x^{-1+2}+3x^{-4+2}\right)\\ y=4\left(x+3x^{-2}\right)\\ y=4x+12x^{-2}\\ \frac{dy}{dx}=\frac{d}{dx}\left(4x+12x^{-2}\right)\\ \frac{dy}{dx}=4\frac{d}{dx}x+\frac{d}{dx}12x^{-2}\\ \frac{dy}{dx}=4+\left(-24x^{-3}\right)\\ \frac{dy}{dx}=4-24x^{-3}\end{array}$

The derivative function of $y=4x^2\left(x^{-1}+3x^{-4}\right)$ is $\frac{dy}{dx}=4-24x^{-3}$ .