What is (\partial)/(\partial y)(xe^{-xy}) ?

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

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(\partial)/(\partial y)(xe^{-xy})

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

- e^{- x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x e^{- x y} (- x)

Simplify

x e^{- x y} (- x) : - e^{- x y} x^{2}

= - e^{- x y} x^{2}

\frac{d}{d x} (\frac{4 x}{e ^{x}})

x \to 0 lim (\frac{1 cos ( 3 x )}{x})

\frac{3 x}{2}

7 e^{2}

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

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