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}

\frac{\partial}{\partial x} (2 x yz + x y^{2} + x z)

\frac{4 x}{x + 2}

x \to o lim (\frac{cos ( x )}{x})

\frac{d}{d x} (arccos (\frac{1 - x}{1 + x}))

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