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Popular >

derivative of \sqrt[4]{x}-3/x

Solution

\frac{d}{d x} (4 x - \frac{3}{x})

Solution

\frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

Solution steps

\frac{d}{d x} (4 x - \frac{3}{x})

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

\frac{1}{4 x ^{\frac{3}{4}}} - (- \frac{3}{x ^{2}}) : \frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

= \frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[4]{x}-3/x ?
The derivative of \sqrt[4]{x}-3/x is (x^2+12x^{3/4})/(4x^{11/4)}
What is the first derivative of \sqrt[4]{x}-3/x ?
The first derivative of \sqrt[4]{x}-3/x is (x^2+12x^{3/4})/(4x^{11/4)}