What is (\partial}{\partial y}(\frac{x+y^2)/z) ?

The answer to (\partial}{\partial y}(\frac{x+y^2)/z) is (2y)/z

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

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

\frac{2 y}{z}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x) = 0

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

= \frac{1}{z} (0 + 2 y)

Simplify

\frac{1}{z} (0 + 2 y) : \frac{2 y}{z}

= \frac{2 y}{z}

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What is (\partial}{\partial y}(\frac{x+y^2)/z) ?
The answer to (\partial}{\partial y}(\frac{x+y^2)/z) is (2y)/z