Question: Evaluate the partial derivatives below at \(P\).

1. \(\frac{\partial z}{\partial x}\) at \(P\), if \(y\) is held constant;
2. \(\frac{\partial z}{\partial x}\) at \(P\), if \(\theta\) is held constant;
3. \(\frac{\partial z}{\partial x}\) at \(P\), if \(r\) is held constant;
4. \(\frac{\partial z}{\partial \theta}\) at \(P\), if \(x\) is held constant;
5. \(\nabla f(P)=\left(f_{x}(P), f_{y}(P)\right)\), where \(f(x, y)=g(r)\).

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