What is (\partial)/(\partial x)(xe^x+2ye^x) ?

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

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(\partial)/(\partial x)(xe^x+2ye^x)

\frac{\partial}{\partial x} (x e^{x} + 2 y e^{x})

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

Solution steps

\frac{\partial}{\partial x} (x e^{x} + 2 y e^{x})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x e^{x}) + \frac{\partial}{\partial x} (2 y e^{x})

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

\frac{\partial}{\partial x} (2 y e^{x}) = 2 y e^{x}

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

\frac{e ^{x} ( x - 2 )}{( x - 1 ) ^{2}}

\int \frac{1}{x ^{2} + 9 x + 18} d x

\int sin (θ) + 1 d θ

\frac{d}{d x} (e^{5 - 7 x})

\int cosh (5 x) d x

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