What is the derivative of-1/(9x^{10/9)} ?

The derivative of-1/(9x^{10/9)} is (10)/(81x^{19/9)}

What is the first derivative of-1/(9x^{10/9)} ?

The first derivative of-1/(9x^{10/9)} is (10)/(81x^{19/9)}

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derivative of

- \frac{1}{9 x ^{\frac{10}{9}}}

\frac{10}{81 x ^{\frac{19}{9}}}

Solution steps

\frac{d}{d x} (- \frac{1}{9 x ^{\frac{10}{9}}})

Take the constant out:

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

= - \frac{1}{9} \frac{d}{d x} (\frac{1}{x ^{\frac{10}{9}}})

Apply exponent rule:

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

= - \frac{1}{9} \frac{d}{d x} (x^{- \frac{10}{9}})

Apply the Power Rule:

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

= - \frac{1}{9} (- \frac{10}{9} x^{- \frac{10}{9} - 1})

Simplify

- \frac{1}{9} (- \frac{10}{9} x^{- \frac{10}{9} - 1}) : \frac{10}{81 x ^{\frac{19}{9}}}

= \frac{10}{81 x ^{\frac{19}{9}}}

What is the derivative of-1/(9x^{10/9)} ?
The derivative of-1/(9x^{10/9)} is (10)/(81x^{19/9)}
What is the first derivative of-1/(9x^{10/9)} ?
The first derivative of-1/(9x^{10/9)} is (10)/(81x^{19/9)}