The derivative of the function is = [tex]-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}[/tex].
What is Derivative?
The derivative is the instantaneous rate of change of a function with respect to one of its variables.
Given function:
y= [tex](x^{-2} + x )^{-3}[/tex]
Differentiating and applying Chain Rule
=[tex]-\frac{3}{\left(x^{-2}+x\right)^4}\frac{d}{dx}\left(x^{-2}+x\right)[/tex]
= [tex]-\frac{3}{\left(x^{-2}+x\right)^4}\left(-\frac{2}{x^3}+1\right)[/tex]
= [tex]-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}[/tex]
Hence, the value of derivative is [tex]-\frac{3x^5\left(x^3-2\right)}{\left(1+x^3\right)^4}[/tex].
Learn more about derivative here:
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