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

The answer to (\partial)/(\partial x)((2-xy)e^{-xy}) is -3e^{-xy}y+e^{-xy}xy^2

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 - x y, g = e^{- x y}

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

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

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

= (- y) e^{- x y} + (- y e^{- y x}) (2 - x y)

Simplify

(- y) e^{- x y} + (- y e^{- y x}) (2 - x y) : - 3 e^{- x y} y + e^{- x y} x y^{2}

= - 3 e^{- x y} y + e^{- x y} x y^{2}

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

\int \frac{2 y}{x ^{2} + 1} d y

\int x + y + z d x

\frac{d}{d x} (- 2 x^{2} + 3 x - 4)

\frac{d y}{d x} = \frac{3 y}{x}, x > 0

What is (\partial)/(\partial x)((2-xy)e^{-xy}) ?
The answer to (\partial)/(\partial x)((2-xy)e^{-xy}) is -3e^{-xy}y+e^{-xy}xy^2