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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial 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}}

y (x + 4) = 1, x = 0, y = 0, x = 4

\int (ln (16 x))^{2} d x

\int (- 6 x^{6} - 2 x^{3} - 4) d x

y = x^{2} - 39, y = 9 - 2 x

\frac{\partial}{\partial y} (12 x y)

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