Question

prove that d/dt (F×G) =F×dG/dt + dF/dt ×G.​

Answer 1

Proof of  d/dt (F×G) =F×dG/dt + dF/dt ×G.​

Explanation:

• d/dt ( F×G) = lim h →0 {F(t+h)×G(t+h) -F(t)G(t)}/h
• Subtract and add at the Top,  F(t+h)G(t)
• Then we will have, lim h ->0 { F(t+h)[ G(t+h) -G(t)] + G(t)[ F(t+h) - F(t)]}/h = lim h->0 F(t+h) [ G(t+h) -G(t)]/h + lim h->0 G(t) [ F(t+h) -F(t)]/h and when       h ->0 ,

• Then we get, F(t)×G'(t) + G(t)×F'(t).