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

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

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

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

\frac{y}{x ^{2} + y ^{2}}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y}{x ^{2} + y ^{2}} - 0

Simplify

= \frac{y}{x ^{2} + y ^{2}}

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