What is (\partial)/(\partial x)(x^2y+3e^{xy}) ?

The answer to (\partial)/(\partial x)(x^2y+3e^{xy}) is 2yx+3e^{xy}y

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(\partial)/(\partial x)(x^2y+3e^{xy})

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

2 y x + 3 e^{x y} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + 3 e^{x y} y

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