What is the derivative of x^{8/9} ?

The derivative of x^{8/9} is 8/(9x^{1/9)}

What is the first derivative of x^{8/9} ?

The first derivative of x^{8/9} is 8/(9x^{1/9)}

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\frac{d}{d x} (x^{\frac{8}{9}})

\frac{8}{9 x ^{\frac{1}{9}}}

Solution steps

\frac{d}{d x} (x^{\frac{8}{9}})

Apply the Power Rule:

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

= \frac{8}{9} x^{\frac{8}{9} - 1}

Simplify

\frac{8}{9} x^{\frac{8}{9} - 1} : \frac{8}{9 x ^{\frac{1}{9}}}

= \frac{8}{9 x ^{\frac{1}{9}}}

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What is the derivative of x^{8/9} ?
The derivative of x^{8/9} is 8/(9x^{1/9)}
What is the first derivative of x^{8/9} ?
The first derivative of x^{8/9} is 8/(9x^{1/9)}