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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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