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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y \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}

= 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

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

Simplify

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

\frac{d}{d x} (ln (8 - 3 x))

(x^{2} - 8 x)^{4}

\frac{d}{d x} (\frac{e ^{x} x - e ^{x}}{x ^{2}})

y = 2^{x}, y = 4^{x}, y = 4

\frac{\partial}{\partial x} (sin (5 x^{4} y - 3 x y^{4}))

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