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

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

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

x \to 7 lim (4)

n = 0 \sum \infty \frac{1}{1 ^{n}}

6 x - x^{2}

\int \frac{14}{x ^{8}} d x

\frac{d y}{d x} = 7 e^{x - y}

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