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Popular >

derivative of 1/(x^2+1/(x^3))

Solution

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

Solution

- \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(x^2+1/(x^3)) ?
The derivative of 1/(x^2+1/(x^3)) is -2/(x^3)-3/(x^4)
What is the first derivative of 1/(x^2+1/(x^3)) ?
The first derivative of 1/(x^2+1/(x^3)) is -2/(x^3)-3/(x^4)