What is (\partial)/(\partial y)(xy^2e^{-xz}) ?

The answer to (\partial)/(\partial y)(xy^2e^{-xz}) is 2e^{-xz}xy

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(\partial)/(\partial y)(xy^2e^{-xz})

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

2 e^{- x z} x y

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 e^{- x z} x y

\frac{\partial}{\partial y} (x^{6} - 8 x^{5} y)

g (x) = 4 x^{2} + 10 x - 1

(x + 2) e^{\frac{1}{x}}

\int_{- 2}^{0} x^{2} + x - 1 d x

x \to 0 lim (\frac{( tan ( 2 x ) )}{x})

What is (\partial)/(\partial y)(xy^2e^{-xz}) ?
The answer to (\partial)/(\partial y)(xy^2e^{-xz}) is 2e^{-xz}xy