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Popular >

derivative of sqrt(1/(x^{31)})

Solution

\frac{d}{d x} (\frac{1}{x ^{31}})

Solution

- \frac{31}{2 x ^{\frac{33}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{31}})

Apply the chain rule:

\frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

= \frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

\frac{d}{d x} (\frac{1}{x ^{31}}) = - \frac{31}{x ^{32}}

= \frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}})

Simplify

\frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}}) : - \frac{31}{2 x ^{\frac{33}{2}}}

= - \frac{31}{2 x ^{\frac{33}{2}}}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1/(x^{31)}) ?
The derivative of sqrt(1/(x^{31)}) is -(31)/(2x^{33/2)}
What is the first derivative of sqrt(1/(x^{31)}) ?
The first derivative of sqrt(1/(x^{31)}) is -(31)/(2x^{33/2)}