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

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

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(\partial)/(\partial x)(ze^{xy})

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

z e^{x y} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= z e^{x y} y

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