What is the derivative of 1/(7x^{6/7)} ?

The derivative of 1/(7x^{6/7)} is -6/(49x^{13/7)}

What is the first derivative of 1/(7x^{6/7)} ?

The first derivative of 1/(7x^{6/7)} is -6/(49x^{13/7)}

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derivative of

\frac{1}{7 x ^{\frac{6}{7}}}

- \frac{6}{49 x ^{\frac{13}{7}}}

Solution steps

\frac{d}{d x} (\frac{1}{7 x ^{\frac{6}{7}}})

Take the constant out:

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

= \frac{1}{7} \frac{d}{d x} (\frac{1}{x ^{\frac{6}{7}}})

Apply exponent rule:

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

= \frac{1}{7} \frac{d}{d x} (x^{- \frac{6}{7}})

Apply the Power Rule:

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

= \frac{1}{7} (- \frac{6}{7} x^{- \frac{6}{7} - 1})

Simplify

\frac{1}{7} (- \frac{6}{7} x^{- \frac{6}{7} - 1}) : - \frac{6}{49 x ^{\frac{13}{7}}}

= - \frac{6}{49 x ^{\frac{13}{7}}}

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What is the derivative of 1/(7x^{6/7)} ?
The derivative of 1/(7x^{6/7)} is -6/(49x^{13/7)}
What is the first derivative of 1/(7x^{6/7)} ?
The first derivative of 1/(7x^{6/7)} is -6/(49x^{13/7)}