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

The derivative of 1/(9x^{8/9}) is -8/(81x^{17/9)}

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

The first derivative of 1/(9x^{8/9}) is -8/(81x^{17/9)}

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\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

- \frac{8}{81 x ^{\frac{17}{9}}}

Solution steps

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

Take the constant out:

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

= \frac{1}{9} \frac{d}{d x} (\frac{1}{x ^{\frac{8}{9}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{1}{9} \frac{d}{d x} (x^{- \frac{8}{9}})

Apply the Power Rule:

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

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

Simplify

\frac{1}{9} (- \frac{8}{9} x^{- \frac{8}{9} - 1}) : - \frac{8}{81 x ^{\frac{17}{9}}}

= - \frac{8}{81 x ^{\frac{17}{9}}}

What is the derivative of 1/(9x^{8/9}) ?
The derivative of 1/(9x^{8/9}) is -8/(81x^{17/9)}
What is the first derivative of 1/(9x^{8/9}) ?
The first derivative of 1/(9x^{8/9}) is -8/(81x^{17/9)}