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

The answer to (\partial)/(\partial x)(xe^x+e^x) is e^xx+2e^x

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

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

e^{x} x + 2 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x} + e^{x} x + e^{x}

Simplify

= e^{x} x + 2 e^{x}

\frac{\partial}{\partial y} (x - 2 y)

y^{^{''}} - 14 y^{^{'}} + 50 y = 0, y (0) = 10, y (\frac{π}{2}) = 3

f (x) = \frac{e ^{x} x - e ^{x}}{x ^{2}}

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

\int x^{4} (1 - x^{2}) d x

What is (\partial)/(\partial x)(xe^x+e^x) ?
The answer to (\partial)/(\partial x)(xe^x+e^x) is e^xx+2e^x