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Popular Calculus >

derivative of sqrt(1/(x^3))

Solution

derivative of

\frac{1}{x ^{3}}

Solution

- \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{3}})

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= \frac{1}{2 \frac{1}{x ^{3}}} (- \frac{3}{x ^{4}})

Simplify

\frac{1}{2 \frac{1}{x ^{3}}} (- \frac{3}{x ^{4}}) : - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

= - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1/(x^3)) ?
The derivative of sqrt(1/(x^3)) is -(3sqrt(x^2))/(2x^{7/2)}
What is the first derivative of sqrt(1/(x^3)) ?
The first derivative of sqrt(1/(x^3)) is -(3sqrt(x^2))/(2x^{7/2)}