What is the derivative of f(x)=36x^{-2}-2x^{-4}+2 ?

The derivative of f(x)=36x^{-2}-2x^{-4}+2 is 8/(x^5)-(72)/(x^3)

What is the first derivative of f(x)=36x^{-2}-2x^{-4}+2 ?

The first derivative of f(x)=36x^{-2}-2x^{-4}+2 is 8/(x^5)-(72)/(x^3)

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derivative of

f (x) = 36 x^{- 2} - 2 x^{- 4} + 2

\frac{8}{x ^{5}} - \frac{72}{x ^{3}}

Solution steps

\frac{d}{d x} (36 x^{- 2} - 2 x^{- 4} + 2)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (36 x^{- 2}) - \frac{d}{d x} (2 x^{- 4}) + \frac{d}{d x} (2)

\frac{d}{d x} (36 x^{- 2}) = - \frac{72}{x ^{3}}

\frac{d}{d x} (2 x^{- 4}) = - \frac{8}{x ^{5}}

\frac{d}{d x} (2) = 0

= - \frac{72}{x ^{3}} - (- \frac{8}{x ^{5}}) + 0

Simplify

= \frac{8}{x ^{5}} - \frac{72}{x ^{3}}

What is the derivative of f(x)=36x^{-2}-2x^{-4}+2 ?
The derivative of f(x)=36x^{-2}-2x^{-4}+2 is 8/(x^5)-(72)/(x^3)
What is the first derivative of f(x)=36x^{-2}-2x^{-4}+2 ?
The first derivative of f(x)=36x^{-2}-2x^{-4}+2 is 8/(x^5)-(72)/(x^3)