What is the derivative of 5x^{-3/5} ?

The derivative of 5x^{-3/5} is -3/(x^{8/5)}

What is the first derivative of 5x^{-3/5} ?

The first derivative of 5x^{-3/5} is -3/(x^{8/5)}

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

- \frac{3}{x ^{\frac{8}{5}}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

5 (- \frac{3}{5} x^{- \frac{3}{5} - 1}) : - \frac{3}{x ^{\frac{8}{5}}}

= - \frac{3}{x ^{\frac{8}{5}}}

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What is the derivative of 5x^{-3/5} ?
The derivative of 5x^{-3/5} is -3/(x^{8/5)}
What is the first derivative of 5x^{-3/5} ?
The first derivative of 5x^{-3/5} is -3/(x^{8/5)}