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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 2 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

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

Simplify

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

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

(x^{3} + 1)^{- 1}

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

y = sin (sin (x))

y^{^{''}} = - 4 y

\int_{0}^{1} \frac{3}{2 t - 5} d t

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