What is the derivative of-1/6 (x^{-6}-x^{12}) ?

The derivative of-1/6 (x^{-6}-x^{12}) is (2x^{18}+1)/(x^7)

What is the first derivative of-1/6 (x^{-6}-x^{12}) ?

The first derivative of-1/6 (x^{-6}-x^{12}) is (2x^{18}+1)/(x^7)

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derivative of

- \frac{1}{6} (x^{- 6} - x^{12})

\frac{2 x ^{18} + 1}{x ^{7}}

Solution steps

\frac{d}{d x} (- \frac{1}{6} (x^{- 6} - x^{12}))

Take the constant out:

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

= - \frac{1}{6} \frac{d}{d x} (x^{- 6} - x^{12})

Apply the Sum/Difference Rule:

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

= - \frac{1}{6} (\frac{d}{d x} (x^{- 6}) - \frac{d}{d x} (x^{12}))

\frac{d}{d x} (x^{- 6}) = - \frac{6}{x ^{7}}

\frac{d}{d x} (x^{12}) = 12 x^{11}

= - \frac{1}{6} (- \frac{6}{x ^{7}} - 12 x^{11})

Simplify

- \frac{1}{6} (- \frac{6}{x ^{7}} - 12 x^{11}) : \frac{2 x ^{18} + 1}{x ^{7}}

= \frac{2 x ^{18} + 1}{x ^{7}}

What is the derivative of-1/6 (x^{-6}-x^{12}) ?
The derivative of-1/6 (x^{-6}-x^{12}) is (2x^{18}+1)/(x^7)
What is the first derivative of-1/6 (x^{-6}-x^{12}) ?
The first derivative of-1/6 (x^{-6}-x^{12}) is (2x^{18}+1)/(x^7)