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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{4 xx - 1 \cdot ( 2 x ^{2} + 1 )}{x ^{2}}

Simplify

\frac{4 xx - 1 \cdot ( 2 x ^{2} + 1 )}{x ^{2}} : \frac{2 x ^{2} - 1}{x ^{2}}

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

Graph

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\int 5 \cdot sin (x) d x

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(x^{2} + 1) \frac{d y}{d x} + 8 x (y - 1) = 0, y (0) = 2

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\int \frac{1}{y ^{\frac{11}{5}}} d y

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Frequently Asked Questions (FAQ)

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