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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{1 + x ^{2}} \cdot 2 y^{2 - 1}

Simplify

\frac{1}{1 + x ^{2}} \cdot 2 y^{2 - 1} : \frac{2 y}{1 + x ^{2}}

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

\int \frac{x - 2}{x ^{2} - 7 x + 12} d x

\frac{d y}{d x} = \frac{x ( 1 + y ^{2} )}{4 y}

\frac{d}{d x} (\frac{x}{2} + \frac{3}{2} + \frac{4}{x + 1})

x (x - 4) y^{^{'}} + y = 0

x ln (2 x)

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