What is (\partial)/(\partial x)((5x+4y)e^y) ?

The answer to (\partial)/(\partial x)((5x+4y)e^y) is 5e^y

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(\partial)/(\partial x)((5x+4y)e^y)

\frac{\partial}{\partial x} ((5 x + 4 y) e^{y})

5 e^{y}

Solution steps

\frac{\partial}{\partial x} ((5 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} (5 x + 4 y)

Apply the Sum/Difference Rule:

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

= e^{y} (\frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (4 y))

\frac{\partial}{\partial x} (5 x) = 5

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

= e^{y} (5 + 0)

Simplify

= 5 e^{y}

5 x^{2} - 4 x + 5

x \to \infty lim (x e^{x})

\frac{d y}{d x} = \frac{9 x}{7 y}

\frac{d}{d y} (ln (x y))

\frac{\partial}{\partial x} (5 cos (x))

What is (\partial)/(\partial x)((5x+4y)e^y) ?
The answer to (\partial)/(\partial x)((5x+4y)e^y) is 5e^y