What is (\partial)/(\partial y)(x^2+xe^{2y}) ?

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

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(\partial)/(\partial y)(x^2+xe^{2y})

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

2 e^{2 y} x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + x e^{2 y} \cdot 2

Simplify

= 2 e^{2 y} x

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

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