What is (\partial)/(\partial x)((3x+4y)e^y) ?

The answer to (\partial)/(\partial x)((3x+4y)e^y) is 3e^y

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(\partial)/(\partial x)((3x+4y)e^y)

\frac{\partial}{\partial x} ((3 x + 4 y) e^{y})

3 e^{y}

Solution steps

\frac{\partial}{\partial x} ((3 x + 4 y) e^{y})

Treat

y

as a constant

Take the constant out:

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

= e^{y} \frac{\partial}{\partial x} (3 x + 4 y)

Apply the Sum/Difference Rule:

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

= e^{y} (\frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (4 y))

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

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

= e^{y} (3 + 0)

Simplify

= 3 e^{y}

\int_{1}^{x} t y + 3 d t

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2 x y d x + (2 + x^{2}) d y = 0

y^{^{''}} - 2 y^{^{'}} = x + 2 e^{x}

\int (x^{2} - \frac{3}{x} + cos (x) - \frac{2}{x}) d x

What is (\partial)/(\partial x)((3x+4y)e^y) ?
The answer to (\partial)/(\partial x)((3x+4y)e^y) is 3e^y