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Popular >

derivative of (x^4/8+(x^{-2})/4)

Solution

\frac{d}{d x} (\frac{x ^{4}}{8} + \frac{x ^{- 2}}{4})

Solution

\frac{x ^{3}}{2} - \frac{1}{2 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{8} + \frac{x ^{- 2}}{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4}}{8}) + \frac{d}{d x} (\frac{x ^{- 2}}{4})

\frac{d}{d x} (\frac{x ^{4}}{8}) = \frac{x ^{3}}{2}

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

= \frac{x ^{3}}{2} - \frac{1}{2 x ^{3}}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of (x^4/8+(x^{-2})/4) ?
The derivative of (x^4/8+(x^{-2})/4) is (x^3)/2-1/(2x^3)
What is the first derivative of (x^4/8+(x^{-2})/4) ?
The first derivative of (x^4/8+(x^{-2})/4) is (x^3)/2-1/(2x^3)