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

The derivative of y=x^{-3}+5x^{-2} is -3/(x^4)-(10)/(x^3)

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

The first derivative of y=x^{-3}+5x^{-2} is -3/(x^4)-(10)/(x^3)

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derivative of

y = x^{- 3} + 5 x^{- 2}

- \frac{3}{x ^{4}} - \frac{10}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (5 x^{- 2}) = - \frac{10}{x ^{3}}

= - \frac{3}{x ^{4}} - \frac{10}{x ^{3}}

What is the derivative of y=x^{-3}+5x^{-2} ?
The derivative of y=x^{-3}+5x^{-2} is -3/(x^4)-(10)/(x^3)
What is the first derivative of y=x^{-3}+5x^{-2} ?
The first derivative of y=x^{-3}+5x^{-2} is -3/(x^4)-(10)/(x^3)