What is the derivative of 8/5 x^{-2/4} ?

The derivative of 8/5 x^{-2/4} is -4/(5x^{3/2)}

What is the first derivative of 8/5 x^{-2/4} ?

The first derivative of 8/5 x^{-2/4} is -4/(5x^{3/2)}

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\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

- \frac{4}{5 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

Take the constant out:

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

= \frac{8}{5} \frac{d}{d x} (x^{- \frac{2}{4}})

Apply the Power Rule:

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

= \frac{8}{5} (- \frac{2}{4} x^{- \frac{2}{4} - 1})

Simplify

\frac{8}{5} (- \frac{2}{4} x^{- \frac{2}{4} - 1}) : - \frac{4}{5 x ^{\frac{3}{2}}}

= - \frac{4}{5 x ^{\frac{3}{2}}}

What is the derivative of 8/5 x^{-2/4} ?
The derivative of 8/5 x^{-2/4} is -4/(5x^{3/2)}
What is the first derivative of 8/5 x^{-2/4} ?
The first derivative of 8/5 x^{-2/4} is -4/(5x^{3/2)}