What is (\partial)/(\partial x)((5x+2y)(e^y)) ?

The answer to (\partial)/(\partial x)((5x+2y)(e^y)) is 5e^y

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(\partial)/(\partial x)((5x+2y)(e^y))

\frac{\partial}{\partial x} ((5 x + 2 y) (e^{y}))

5 e^{y}

Solution steps

\frac{\partial}{\partial x} ((5 x + 2 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 + 2 y)

Apply the Sum/Difference Rule:

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

= e^{y} (\frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (2 y))

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

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

= e^{y} (5 + 0)

Simplify

= 5 e^{y}

2 x^{2} + 2 x

\int e^{6 x} sin (3 x) d x

\frac{\partial}{\partial x} (x ln (\frac{x}{y ^{2}}))

n \to \infty lim (ln (2))

\frac{d y}{d x} + 4 x y = 8 x^{3}

What is (\partial)/(\partial x)((5x+2y)(e^y)) ?
The answer to (\partial)/(\partial x)((5x+2y)(e^y)) is 5e^y