What is the derivative of 1/2 x^{4/5} ?

The derivative of 1/2 x^{4/5} is 2/(5x^{1/5)}

What is the first derivative of 1/2 x^{4/5} ?

The first derivative of 1/2 x^{4/5} is 2/(5x^{1/5)}

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\frac{d}{d x} (\frac{1}{2} x^{\frac{4}{5}})

\frac{2}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (\frac{1}{2} x^{\frac{4}{5}})

Take the constant out:

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

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

Apply the Power Rule:

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

= \frac{1}{2} \cdot \frac{4}{5} x^{\frac{4}{5} - 1}

Simplify

\frac{1}{2} \cdot \frac{4}{5} x^{\frac{4}{5} - 1} : \frac{2}{5 x ^{\frac{1}{5}}}

= \frac{2}{5 x ^{\frac{1}{5}}}

What is the derivative of 1/2 x^{4/5} ?
The derivative of 1/2 x^{4/5} is 2/(5x^{1/5)}
What is the first derivative of 1/2 x^{4/5} ?
The first derivative of 1/2 x^{4/5} is 2/(5x^{1/5)}