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

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

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

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

e^{y} z

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z e^{y} (1 + 0)

Simplify

= e^{y} z

(1 + 5)^{4}

y (2 x - y + 1) d x - x (3 x - 4 y + 3) d y

6 (2 - 2 - 6 - 3)

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

\frac{( 6 - x - 3 ) ( 1 - x + 2 )}{- x - 3}

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