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

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

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

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

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

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

Simplify

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

x \to 1 lim (\frac{x ^{2} + 7 x}{x})

t^{3}

\int_{- \infty}^{0} \frac{1}{3 - 6 x} d x

y = e^{x}, y = e^{2 x}, x = ln (4)

(cos (\frac{1}{x}))^{^{'}}

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