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

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

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(\partial)/(\partial x)((x+y)*e^y)

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

e^{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= e^{y} (1 + 0)

Simplify

= e^{y}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (x)

1 - 6 x

y = 3 x, y = \frac{3 x}{4}

\frac{d}{d x} (arcsec (3 x^{2} + 1))

x \to \infty lim (n c^{n})

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