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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{( 4 x ^{2} + 2 x + 2 )}{x}

\int x 2 x - 1 d x

\int \frac{4 x}{3 x ^{2}} d x

f (x) = \frac{x}{x + 7}

\int in (x + x^{2} + 1) d x

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