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

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

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

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

e^{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 y) = 0

= e^{y} + 0

Simplify

= e^{y}

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1.12 x^{3} - 6.3 x^{2} - 11.2 x + 1.2

x^{2} e^{x}

\frac{d}{d x} (\frac{i + x j + 2 x k}{5 x ^{2} + 1})

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