What is (\partial)/(\partial y)(3xe^{-2xy}) ?

The answer to (\partial)/(\partial y)(3xe^{-2xy}) is -6e^{-2xy}x^2

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(\partial)/(\partial y)(3xe^{-2xy})

\frac{\partial}{\partial y} (3 x e^{- 2 x y})

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

Solution steps

\frac{\partial}{\partial y} (3 x e^{- 2 x y})

Treat

x

as a constant

Take the constant out:

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

= 3 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

= 3 x e^{- 2 x y} (- 2 x)

Simplify

3 x e^{- 2 x y} (- 2 x) : - 6 e^{- 2 x y} x^{2}

= - 6 e^{- 2 x y} x^{2}

What is (\partial)/(\partial y)(3xe^{-2xy}) ?
The answer to (\partial)/(\partial y)(3xe^{-2xy}) is -6e^{-2xy}x^2