What is (\partial)/(\partial x)(ye^{-xy}) ?

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

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(\partial)/(\partial x)(ye^{-xy})

\frac{\partial}{\partial x} (y 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{\partial}{\partial x} (\frac{x}{x + 1})

x \to \infty lim (x (1)^{x})

\int e^{8 θ} sin (9 θ) d θ

12 e^{x}

\frac{x ^{2} + x - 2}{x ^{3} + 6}

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