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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y}, g = x

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

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

\frac{\partial}{\partial x} (x) = 1

= y (e^{x y} y x + 1 \cdot e^{x y})

Simplify

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

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