What is (\partial)/(\partial z)(x^2+(y-1)^2+z^2) ?

The answer to (\partial)/(\partial z)(x^2+(y-1)^2+z^2) is 2z

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(\partial)/(\partial z)(x^2+(y-1)^2+z^2)

\frac{\partial}{\partial z} (x^{2} + (y - 1)^{2} + z^{2})

2 z

Solution steps

\frac{\partial}{\partial z} (x^{2} + (y - 1)^{2} + z^{2})

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x^{2}) + \frac{\partial}{\partial z} ((y - 1)^{2}) + \frac{\partial}{\partial z} (z^{2})

\frac{\partial}{\partial z} (x^{2}) = 0

\frac{\partial}{\partial z} ((y - 1)^{2}) = 0

\frac{\partial}{\partial z} (z^{2}) = 2 z

= 0 + 0 + 2 z

Simplify

= 2 z

f (y) = 5 x + \frac{135}{x} (15 x + 30)

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{4})

x \to 2 - lim (\frac{m x - 3 m}{x - 3})

\int \frac{4 e ^{x}}{e ^{x} + 3} d x

\frac{d}{d x} (x^{\frac{4}{5}} (x - 4)^{2})

What is (\partial)/(\partial z)(x^2+(y-1)^2+z^2) ?
The answer to (\partial)/(\partial z)(x^2+(y-1)^2+z^2) is 2z