SOLUTION:
Example 4 __
If , find .
SOLUTION:
Example 5 __
If s(t) = ( t 2 + 1 )(1 − t)^2 , find s′(t).
SOLUTION: s′(t) = ( t 2 + 1 ) · 2(1 − t)(−1) + (1 − t)^2 · 2 t (Product Rule)
= 2(1 − t)( −1 + t − 2t 2 ).Example 6 __
If f (t) = e 2 t sin 3t, find f ′(0).
SOLUTION: f ′(t) = e 2 t(cos 3t · 3) + sin 3t(e 2 t · 2) (Product Rule)
= e 2 t(3 cos 3t + 2 sin 3t)
Then, f ′(0) = 1(3 · 1 + 2 · 0) = 3.Example 7 __
If , find f ′(v).