Question: Let (F, G) be smooth, bounded cylindrical functions. Show that a) (D_{t}(F G)=G D_{t} F+F D_{t} G). b) (D_{t}^{m}(F G)=sum_{k=0}^{m}left(begin{array}{c}m kend{array}ight) D_{t}^{k} F cdot

Let \(F, G\) be smooth, bounded cylindrical functions. Show that

a) \(D_{t}(F G)=G D_{t} F+F D_{t} G\).

b) \(D_{t}^{m}(F G)=\sum_{k=0}^{m}\left(\begin{array}{c}m \\ k\end{array}ight) D_{t}^{k} F \cdot D_{t}^{m-k} G\).

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