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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

\int \frac{3}{2 x} d x

\frac{d y}{d x} = \frac{x e ^{3 x + y^{3}}}{y ^{2}}

\frac{d}{d x} ((3 x^{3} - 4) (- 4 x - 3))

4 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

\int 1 x d x

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