What is (\partial)/(\partial x)(xye^{x+2y}) ?

The answer to (\partial)/(\partial x)(xye^{x+2y}) is y(e^{x+2y}+e^{x+2y}x)

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(\partial)/(\partial x)(xye^{x+2y})

\frac{\partial}{\partial x} (x y e^{x + 2 y})

y (e^{x + 2 y} + e^{x + 2 y} x)

Solution steps

\frac{\partial}{\partial x} (x y e^{x + 2 y})

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x e^{x + 2 y})

Apply the Product Rule:

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

f = x, g = e^{x + 2 y}

= y (\frac{\partial}{\partial x} (x) e^{x + 2 y} + \frac{\partial}{\partial x} (e^{x + 2 y}) x)

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

\frac{\partial}{\partial x} (e^{x + 2 y}) = e^{x + 2 y}

= y (1 \cdot e^{x + 2 y} + e^{x + 2 y} x)

Simplify

= y (e^{x + 2 y} + e^{x + 2 y} x)

\frac{d}{d x} (2 x - \frac{1}{x ^{2}})

\frac{d y}{d t}, y = e^{t}

\int sin^{5} (x) d x

\int sec^{2} (x) d x

\frac{d y}{d x} = \frac{y + 2}{x + 7}

What is (\partial)/(\partial x)(xye^{x+2y}) ?
The answer to (\partial)/(\partial x)(xye^{x+2y}) is y(e^{x+2y}+e^{x+2y}x)