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

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

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

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

e^{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (y) = 0

= e^{y} (1 + 0)

Simplify

= e^{y}

\int \frac{k}{r} (- \frac{r ^{2}}{4}) d r

\int \frac{1}{x ^{2} 400 - x ^{2}} d x

\frac{d}{d x} ((2 x^{3} + 4) (x^{4} - 4 x))

\int_{0}^{1} \frac{5}{1 - x ^{2}} d x

y = (x + 5) (x^{3} - 1) (x^{2} - x + 3)

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