Question

Find the derivative of the problem below and show your work

Answer 1

The derivative of the function is =   $-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}$.

What is Derivative?

The derivative is the instantaneous rate of change of a function with respect to one of its variables.

Given function:

y= $(x^{-2} + x )^{-3}$

Differentiating and applying Chain Rule

=$-\frac{3}{\left(x^{-2}+x\right)^4}\frac{d}{dx}\left(x^{-2}+x\right)$

= $-\frac{3}{\left(x^{-2}+x\right)^4}\left(-\frac{2}{x^3}+1\right)$

= $-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}$

Hence, the value of derivative is   $-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}$.

Learn more about derivative here:

brainly.com/question/124529

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