What is (\partial)/(\partial x)((2x+y-4)e^{2y}) ?

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

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

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

2 e^{2 y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (4) = 0

= e^{2 y} (2 + 0 - 0)

Simplify

= 2 e^{2 y}

\int \frac{x - 2}{3 x ^{2} - 12 x + 1} d x

\frac{\partial}{\partial x} (x^{12} e^{x y})

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(x csc (\frac{y}{x}) - y) d x + x d y = 0

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