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Popular >

derivative of x/(2+x^2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

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derivative of (3sqrt(x)+7)x^2 derivative of

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\frac{d}{d x} (- \frac{32}{x ^{3}} + \frac{4}{x ^{2}})

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\int_{2}^{4} \frac{x ^{2} + 1}{x ^{2} - 5} d x

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\int x^{3} cos (x^{2}) d x

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\int x x - 9 d x

Frequently Asked Questions (FAQ)

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