What is (\partial)/(\partial x)(y*e^{-xy}) ?

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

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(\partial)/(\partial x)(y*e^{-xy})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (3 + sin (x))

\frac{d}{d x} (2 cos (π x))

x \to 0 lim (\frac{1}{( x - 1 ) ^{2}})

\frac{\partial}{\partial y} (3 x y)

x \to 0 + lim (x ln (x^{8}))

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