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

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

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

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

- e^{y x} - e^{y x} y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - (e^{y x} + y e^{y x} x)

Simplify

= - e^{y x} - e^{y x} y x

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