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

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

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

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

e^{z}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial z} (e^{z}) = e^{z}

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

= 0 + e^{z} + 0

Simplify

= e^{z}

x y^{^{'}} + ln (x) y = 0

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 2

x \to 4 - lim (\frac{x + 5}{x - 4})

y = x^{2} + 2 x - 1, (1, 2)

x, y = 2, x = 0

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