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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int \frac{1}{P} d P

f (t) = 0.1 (400 - 40 t + t^{2})

\frac{d}{d x} (x + 2 sin (x))

\int \frac{1}{cos ^{2} ( t ) \cdot 1 + tan ( t )} d t

x \to 7 - lim (\frac{∣ x - 7 ∣}{x - 7})

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