Question: Use the chain rule to find \(\frac{dw}{dt}\), where:

\(\begin{aligned} & w={{x}^{2}}+{{y}^{2}}+{{z}^{2}} \\ & x={{e}^{t}}\cos t \\ & y={{e}^{t}}\sin t \\ & z={{e}^{t}} \\ \end{aligned}\)

and t = 0.