What is the derivative of-1/3 (x^{-3}-x^6) ?

The derivative of-1/3 (x^{-3}-x^6) is (2x^9+1)/(x^4)

What is the first derivative of-1/3 (x^{-3}-x^6) ?

The first derivative of-1/3 (x^{-3}-x^6) is (2x^9+1)/(x^4)

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\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

\frac{2 x ^{9} + 1}{x ^{4}}

Solution steps

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

Take the constant out:

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

= - \frac{1}{3} \frac{d}{d x} (x^{- 3} - x^{6})

Apply the Sum/Difference Rule:

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

= - \frac{1}{3} (\frac{d}{d x} (x^{- 3}) - \frac{d}{d x} (x^{6}))

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

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

= - \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5})

Simplify

- \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5}) : \frac{2 x ^{9} + 1}{x ^{4}}

= \frac{2 x ^{9} + 1}{x ^{4}}

What is the derivative of-1/3 (x^{-3}-x^6) ?
The derivative of-1/3 (x^{-3}-x^6) is (2x^9+1)/(x^4)
What is the first derivative of-1/3 (x^{-3}-x^6) ?
The first derivative of-1/3 (x^{-3}-x^6) is (2x^9+1)/(x^4)