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} \cdot 2 x

Simplify

x e^{2 x y} \cdot 2 x : 2 e^{2 x y} x^{2}

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

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