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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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\frac{\partial}{\partial y} (5)

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