What is (\partial)/(\partial x)((x^2)/(x^2+1)) ?

The answer to (\partial)/(\partial x)((x^2)/(x^2+1)) is (2x)/((x^2+1)^2)

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(\partial)/(\partial x)((x^2)/(x^2+1))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

Simplify

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

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

(\frac{f ( t )}{g ( t )})^{'}

\frac{d}{d x} (x e^{x^{2}} (x^{2} + 1)^{10})

x \frac{d y}{d x} = 2 x^{2} + y, y (1) = 3

n = 2 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

n = 1 \sum \infty \frac{5 n}{3 n - 1}

What is (\partial)/(\partial x)((x^2)/(x^2+1)) ?
The answer to (\partial)/(\partial x)((x^2)/(x^2+1)) is (2x)/((x^2+1)^2)