What is (\partial)/(\partial y)((xy^2)/(t+2z)) ?

The answer to (\partial)/(\partial y)((xy^2)/(t+2z)) is (2xy)/(t+2z)

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(\partial)/(\partial y)((xy^2)/(t+2z))

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

\frac{2 x y}{t + 2 z}

Solution steps

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

Treat

x, t, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{2 x y}{t + 2 z}

What is (\partial)/(\partial y)((xy^2)/(t+2z)) ?
The answer to (\partial)/(\partial y)((xy^2)/(t+2z)) is (2xy)/(t+2z)