What is the derivative of f(x)=-1/7 (x^{-7}-x^{14}) ?

The derivative of f(x)=-1/7 (x^{-7}-x^{14}) is (2x^{21}+1)/(x^8)

What is the first derivative of f(x)=-1/7 (x^{-7}-x^{14}) ?

The first derivative of f(x)=-1/7 (x^{-7}-x^{14}) is (2x^{21}+1)/(x^8)

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derivative of

f (x) = - \frac{1}{7} (x^{- 7} - x^{14})

\frac{2 x ^{21} + 1}{x ^{8}}

Solution steps

\frac{d}{d x} (- \frac{1}{7} (x^{- 7} - x^{14}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{7} \frac{d}{d x} (x^{- 7} - x^{14})

Apply the Sum/Difference Rule:

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

= - \frac{1}{7} (\frac{d}{d x} (x^{- 7}) - \frac{d}{d x} (x^{14}))

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

\frac{d}{d x} (x^{14}) = 14 x^{13}

= - \frac{1}{7} (- \frac{7}{x ^{8}} - 14 x^{13})

Simplify

- \frac{1}{7} (- \frac{7}{x ^{8}} - 14 x^{13}) : \frac{2 x ^{21} + 1}{x ^{8}}

= \frac{2 x ^{21} + 1}{x ^{8}}

What is the derivative of f(x)=-1/7 (x^{-7}-x^{14}) ?
The derivative of f(x)=-1/7 (x^{-7}-x^{14}) is (2x^{21}+1)/(x^8)
What is the first derivative of f(x)=-1/7 (x^{-7}-x^{14}) ?
The first derivative of f(x)=-1/7 (x^{-7}-x^{14}) is (2x^{21}+1)/(x^8)