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

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

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

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

e^{x y} + e^{x y} x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y x} + y e^{y x} x + 0

Simplify

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

\int e^{1 - 2 t} d t

\int 2 - 3 x d x

\frac{\partial}{\partial x} (4 y^{8} + 3 y^{2} x^{2})

(x^{2} + y^{2}) d x = 2 x y d y

ln (1 + e^{- x})

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