What is the derivative of x^{-3}+x^{-5}-2x^{-6} ?

The derivative of x^{-3}+x^{-5}-2x^{-6} is -3/(x^4)-5/(x^6)+(12)/(x^7)

What is the first derivative of x^{-3}+x^{-5}-2x^{-6} ?

The first derivative of x^{-3}+x^{-5}-2x^{-6} is -3/(x^4)-5/(x^6)+(12)/(x^7)

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\frac{d}{d x} (x^{- 3} + x^{- 5} - 2 x^{- 6})

- \frac{3}{x ^{4}} - \frac{5}{x ^{6}} + \frac{12}{x ^{7}}

Solution steps

\frac{d}{d x} (x^{- 3} + x^{- 5} - 2 x^{- 6})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{- 3}) + \frac{d}{d x} (x^{- 5}) - \frac{d}{d x} (2 x^{- 6})

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

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

\frac{d}{d x} (2 x^{- 6}) = - \frac{12}{x ^{7}}

= - \frac{3}{x ^{4}} - \frac{5}{x ^{6}} - (- \frac{12}{x ^{7}})

Simplify

= - \frac{3}{x ^{4}} - \frac{5}{x ^{6}} + \frac{12}{x ^{7}}

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What is the derivative of x^{-3}+x^{-5}-2x^{-6} ?
The derivative of x^{-3}+x^{-5}-2x^{-6} is -3/(x^4)-5/(x^6)+(12)/(x^7)
What is the first derivative of x^{-3}+x^{-5}-2x^{-6} ?
The first derivative of x^{-3}+x^{-5}-2x^{-6} is -3/(x^4)-5/(x^6)+(12)/(x^7)