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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= - 2 (1 \cdot e^{- x y} + (- y e^{- y x}) x)

Simplify

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

\frac{d y}{d x} - 2 x y = x

\frac{d y}{d x} + y - cos (x) = 0

f (x) = x^{3} (x - 1)^{2}

- 10 ln (x e^{x^{8}})

n = 1 \sum \infty in (\frac{1}{n})

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