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

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

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

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

2 e^{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 e^{2}) = 0

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

= 0 + 2 e^{y}

Simplify

= 2 e^{y}

\int_{2}^{\infty} \frac{1}{x ^{5}} d x

x^{2}, x + 6

\int x e^{\frac{x ^{2}}{2}} d x

\frac{d}{d x} (2 x \cdot e^{3 x})

x \to π lim (3 arctan (x))

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