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derivative of (x^3/4+1/(3x))

Solution

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

Solution

\frac{3 x ^{2}}{4} - \frac{1}{3 x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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