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

\int \frac{8}{( x - 5 ) ( x + 3 )} d x

\int e^{x} \cdot ln (x) d x

n = 1 \sum \infty \frac{n}{e ^{n^{2}}}

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (y))

x \to 0 lim (\frac{x ^{3} + 7 x}{x})

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