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Popular >

derivative of sqrt(1/(x^{27)})

Solution

\frac{d}{d x} (\frac{1}{x ^{27}})

Solution

- \frac{27}{2 x ^{\frac{29}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{27}})

Apply the chain rule:

\frac{1}{2 \frac{1}{x ^{27}}} \frac{d}{d x} (\frac{1}{x ^{27}})

= \frac{1}{2 \frac{1}{x ^{27}}} \frac{d}{d x} (\frac{1}{x ^{27}})

\frac{d}{d x} (\frac{1}{x ^{27}}) = - \frac{27}{x ^{28}}

= \frac{1}{2 \frac{1}{x ^{27}}} (- \frac{27}{x ^{28}})

Simplify

\frac{1}{2 \frac{1}{x ^{27}}} (- \frac{27}{x ^{28}}) : - \frac{27}{2 x ^{\frac{29}{2}}}

= - \frac{27}{2 x ^{\frac{29}{2}}}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1/(x^{27)}) ?
The derivative of sqrt(1/(x^{27)}) is -(27)/(2x^{29/2)}
What is the first derivative of sqrt(1/(x^{27)}) ?
The first derivative of sqrt(1/(x^{27)}) is -(27)/(2x^{29/2)}