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

The answer to (\partial)/(\partial x)(sin(xe^{xy})) is cos(xe^{xy})(e^{yx}+ye^{yx}x)

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(\partial)/(\partial x)(sin(xe^{xy}))

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

cos (x e^{x y}) (e^{y x} + y e^{y x} x)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (x e^{x y}) (e^{y x} + y e^{y x} x)

What is (\partial)/(\partial x)(sin(xe^{xy})) ?
The answer to (\partial)/(\partial x)(sin(xe^{xy})) is cos(xe^{xy})(e^{yx}+ye^{yx}x)