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

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

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

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

\frac{2 y}{x + 1}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

3 sin (θ)

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\frac{\partial}{\partial x} (x^{0.6} \cdot y^{0.4})

\int 4 x (x^{2} + 30000)^{- \frac{2}{3}} d x

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