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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\frac{d}{d x} (\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}}}

x^{3} \frac{d y}{d x} = y^{2} (x - 4)

\int \frac{1}{a ( sec ( x ) )} d x

\frac{d}{d x} (\frac{1 x + 1 + x}{x ^{2} - 1})

h

[x + (x + sin^{2} (x))^{4}]^{3}

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)}