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

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

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

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

e^{x y - y} y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x y - y} y

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