What is (\partial)/(\partial x)(3x+y+e^x+2e^y) ?

The answer to (\partial)/(\partial x)(3x+y+e^x+2e^y) is e^x+3

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(\partial)/(\partial x)(3x+y+e^x+2e^y)

\frac{\partial}{\partial x} (3 x + y + e^{x} + 2 e^{y})

e^{x} + 3

Solution steps

\frac{\partial}{\partial x} (3 x + y + e^{x} + 2 e^{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (e^{x}) + \frac{\partial}{\partial x} (2 e^{y})

\frac{\partial}{\partial x} (3 x) = 3

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

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

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

= 3 + 0 + e^{x} + 0

Simplify

= e^{x} + 3

What is (\partial)/(\partial x)(3x+y+e^x+2e^y) ?
The answer to (\partial)/(\partial x)(3x+y+e^x+2e^y) is e^x+3