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Popular >

derivative of x/(x^2+1)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Graph

Popular Examples

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\int (5 + cot^{2} (x)) d x

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\frac{s}{s ^{2} + 2 s}

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x \to \infty lim (5 + \frac{3}{x})

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\int 15 tan^{2} (x se) c^{3} x

Frequently Asked Questions (FAQ)

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