What is the derivative of X^{1/5} ?

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

What is the first derivative of X^{1/5} ?

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

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derivative of

X^{\frac{1}{5}}

\frac{1}{5 X ^{\frac{4}{5}}}

Solution steps

\frac{d}{d X} (X^{\frac{1}{5}})

Apply the Power Rule:

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

= \frac{1}{5} X^{\frac{1}{5} - 1}

Simplify

\frac{1}{5} X^{\frac{1}{5} - 1} : \frac{1}{5 X ^{\frac{4}{5}}}

= \frac{1}{5 X ^{\frac{4}{5}}}

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