Question: Use the chain rule to find the indicated derivatives.

1. \(\left.\frac{d z}{d t}\right|_{t=0}\), when \(z=\sqrt{1+x^{2}+y^{2}}, x=\cos (2 t), y=3 \sin \left(t^{2}\right)\)
2. \(\frac{\partial w}{\partial u}\) and \(\frac{\partial \mathrm{w}}{\partial \mathrm{v}}\), when \(w=e^{x+2 y}, x=\frac{u}{v}, y=\frac{v}{u}\)

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