What is the derivative of sqrt(1/(x^{25)}) ?

The derivative of sqrt(1/(x^{25)}) is -(25)/(2x^{27/2)}

What is the first derivative of sqrt(1/(x^{25)}) ?

The first derivative of sqrt(1/(x^{25)}) is -(25)/(2x^{27/2)}

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\frac{d}{d x} (\frac{1}{x ^{25}})

- \frac{25}{2 x ^{\frac{27}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{25}})

Apply the chain rule:

\frac{1}{2 \frac{1}{x ^{25}}} \frac{d}{d x} (\frac{1}{x ^{25}})

= \frac{1}{2 \frac{1}{x ^{25}}} \frac{d}{d x} (\frac{1}{x ^{25}})

\frac{d}{d x} (\frac{1}{x ^{25}}) = - \frac{25}{x ^{26}}

= \frac{1}{2 \frac{1}{x ^{25}}} (- \frac{25}{x ^{26}})

Simplify

\frac{1}{2 \frac{1}{x ^{25}}} (- \frac{25}{x ^{26}}) : - \frac{25}{2 x ^{\frac{27}{2}}}

= - \frac{25}{2 x ^{\frac{27}{2}}}

What is the derivative of sqrt(1/(x^{25)}) ?
The derivative of sqrt(1/(x^{25)}) is -(25)/(2x^{27/2)}
What is the first derivative of sqrt(1/(x^{25)}) ?
The first derivative of sqrt(1/(x^{25)}) is -(25)/(2x^{27/2)}