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

The derivative of 1/(10x^{9/10)} is -9/(100x^{19/10)}

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

The first derivative of 1/(10x^{9/10)} is -9/(100x^{19/10)}

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derivative of

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

- \frac{9}{100 x ^{\frac{19}{10}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{10} (- \frac{9}{10} x^{- \frac{9}{10} - 1}) : - \frac{9}{100 x ^{\frac{19}{10}}}

= - \frac{9}{100 x ^{\frac{19}{10}}}

What is the derivative of 1/(10x^{9/10)} ?
The derivative of 1/(10x^{9/10)} is -9/(100x^{19/10)}
What is the first derivative of 1/(10x^{9/10)} ?
The first derivative of 1/(10x^{9/10)} is -9/(100x^{19/10)}