What is the derivative of x^{-3}+1/(x^7) ?

The derivative of x^{-3}+1/(x^7) is -3/(x^4)-7/(x^8)

What is the first derivative of x^{-3}+1/(x^7) ?

The first derivative of x^{-3}+1/(x^7) is -3/(x^4)-7/(x^8)

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\frac{d}{d x} (x^{- 3} + \frac{1}{x ^{7}})

- \frac{3}{x ^{4}} - \frac{7}{x ^{8}}

Solution steps

\frac{d}{d x} (x^{- 3} + \frac{1}{x ^{7}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{- 3}) + \frac{d}{d x} (\frac{1}{x ^{7}})

\frac{d}{d x} (x^{- 3}) = - \frac{3}{x ^{4}}

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

= - \frac{3}{x ^{4}} - \frac{7}{x ^{8}}

What is the derivative of x^{-3}+1/(x^7) ?
The derivative of x^{-3}+1/(x^7) is -3/(x^4)-7/(x^8)
What is the first derivative of x^{-3}+1/(x^7) ?
The first derivative of x^{-3}+1/(x^7) is -3/(x^4)-7/(x^8)