What is the derivative of-1/5 (x^{-5}-x^{10}) ?

The derivative of-1/5 (x^{-5}-x^{10}) is (2x^{15}+1)/(x^6)

What is the first derivative of-1/5 (x^{-5}-x^{10}) ?

The first derivative of-1/5 (x^{-5}-x^{10}) is (2x^{15}+1)/(x^6)

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\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

\frac{2 x ^{15} + 1}{x ^{6}}

Solution steps

\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

Take the constant out:

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

= - \frac{1}{5} \frac{d}{d x} (x^{- 5} - x^{10})

Apply the Sum/Difference Rule:

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

= - \frac{1}{5} (\frac{d}{d x} (x^{- 5}) - \frac{d}{d x} (x^{10}))

\frac{d}{d x} (x^{- 5}) = - \frac{5}{x ^{6}}

\frac{d}{d x} (x^{10}) = 10 x^{9}

= - \frac{1}{5} (- \frac{5}{x ^{6}} - 10 x^{9})

Simplify

- \frac{1}{5} (- \frac{5}{x ^{6}} - 10 x^{9}) : \frac{2 x ^{15} + 1}{x ^{6}}

= \frac{2 x ^{15} + 1}{x ^{6}}

What is the derivative of-1/5 (x^{-5}-x^{10}) ?
The derivative of-1/5 (x^{-5}-x^{10}) is (2x^{15}+1)/(x^6)
What is the first derivative of-1/5 (x^{-5}-x^{10}) ?
The first derivative of-1/5 (x^{-5}-x^{10}) is (2x^{15}+1)/(x^6)