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Popular >

derivative of (x^2+1/x)

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Graph

Popular Examples

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n = 1 \sum \infty (- 5)^{n}

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\int cosh (0)

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\int (3 cos (2 θ)) d θ

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

Frequently Asked Questions (FAQ)

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