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

The answer to (\partial)/(\partial y)(x+e^z+y) is 1

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

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

1

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 + 0 + 1

Simplify

= 1

\frac{x}{x + 4}, at 1, 0.2

3 x + 4, at x = 7

x \to 0 - lim (x ln (- x))

\frac{d}{d x} (x + sin^{2} (\frac{x}{3}) - 8)

\frac{d}{d x} (- 3^{x})

What is (\partial)/(\partial y)(x+e^z+y) ?
The answer to (\partial)/(\partial y)(x+e^z+y) is 1