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

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

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

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

2 e^{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y} (2 + 0)

Simplify

= 2 e^{y}

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