What is (\partial)/(\partial z)(x-z-arctan(yz)) ?

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

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(\partial)/(\partial z)(x-z-arctan(yz))

\frac{\partial}{\partial z} (x - z - arctan (yz))

- \frac{y}{z ^{2} y ^{2} + 1} - 1

Solution steps

\frac{\partial}{\partial z} (x - z - arctan (yz))

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} (z) - \frac{\partial}{\partial z} (arctan (yz))

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

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

\frac{\partial}{\partial z} (arctan (yz)) = \frac{y}{y ^{2} z ^{2} + 1}

= 0 - 1 - \frac{y}{y ^{2} z ^{2} + 1}

Simplify

= - \frac{y}{z ^{2} y ^{2} + 1} - 1

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