What is (\partial)/(\partial x)(4e^x-2xe^y) ?

The answer to (\partial)/(\partial x)(4e^x-2xe^y) is 4e^x-2e^y

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(\partial)/(\partial x)(4e^x-2xe^y)

\frac{\partial}{\partial x} (4 e^{x} - 2 x e^{y})

4 e^{x} - 2 e^{y}

Solution steps

\frac{\partial}{\partial x} (4 e^{x} - 2 x e^{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 e^{x}) - \frac{\partial}{\partial x} (2 x e^{y})

\frac{\partial}{\partial x} (4 e^{x}) = 4 e^{x}

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

= 4 e^{x} - 2 e^{y}

What is (\partial)/(\partial x)(4e^x-2xe^y) ?
The answer to (\partial)/(\partial x)(4e^x-2xe^y) is 4e^x-2e^y