Given:
[tex]f(x)=x^2-2x-8x^{-2}+7x^{-3}[/tex]
Required:
We need to differentiate the given function.
Explanation:
[tex]Use\text{ }\frac{d}{dx}(x^n)=nx^{n-1}.[/tex]
Differentiate the given function with respect to x.
[tex]f^{\prime}(x)=2x^{2-1}-2x^{1-1}-8(-2)x^{-2-1}+7(-3)x^{-3-1}[/tex]
[tex]f^{\prime}(x)=2x-2x^0-8(-2)x^{-3}+7(-3)x^{-4}[/tex]
[tex]f^{\prime}(x)=2x-2(1)+16x^{-3}-21x^{-4}[/tex]
[tex]f^{\prime}(x)=2x-2+16x^{-3}-21x^{-4}[/tex]
Final answer:
[tex]f^{\prime}(x)=2x-2+16x^{-3}-21x^{-4}[/tex]
