What is the derivative of 1/(sqrt(x^7)) ?

The derivative of 1/(sqrt(x^7)) is -7/(2x^{9/2)}

What is the first derivative of 1/(sqrt(x^7)) ?

The first derivative of 1/(sqrt(x^7)) is -7/(2x^{9/2)}

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

- \frac{7}{2 x ^{\frac{9}{2}}}

Solution steps

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

Apply exponent rule:

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

= \frac{d}{d x} ((x^{7})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{7})

= - \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{7})

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

= - \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \cdot 7 x^{6}

Simplify

- \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \cdot 7 x^{6} : - \frac{7}{2 x ^{\frac{9}{2}}}

= - \frac{7}{2 x ^{\frac{9}{2}}}

\frac{4 s}{s ^{2} + 8 s + 20}

\frac{d}{d x} ((3 x^{2} - 6 x - sin (x))^{4})

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What is the derivative of 1/(sqrt(x^7)) ?
The derivative of 1/(sqrt(x^7)) is -7/(2x^{9/2)}
What is the first derivative of 1/(sqrt(x^7)) ?
The first derivative of 1/(sqrt(x^7)) is -7/(2x^{9/2)}