What is (\partial)/(\partial y)(x*y^2*e^z) ?

The answer to (\partial)/(\partial y)(x*y^2*e^z) is 2e^zxy

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(\partial)/(\partial y)(xy^2e^z)

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

2 e^{z} x y

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

= x e^{z} \cdot 2 y^{2 - 1}

Simplify

= 2 e^{z} x y

What is (\partial)/(\partial y)(x*y^2*e^z) ?
The answer to (\partial)/(\partial y)(x*y^2*e^z) is 2e^zxy