Barrons AP Calculus - David Bock

SOLUTION:

EXAMPLE 4

SOLUTION:

EXAMPLE 5

If s(t) = (t^2 + 1)(1 − t)^2 , find s ′(t).
SOLUTION:

EXAMPLE 6

If f (t) = e^2 t sin 3t, find f ′(0).

SOLUTION:

Then, f ′(0) = 1(3 · 1 + 2 · 0) = 3.

EXAMPLE 7

SOLUTION:

Note that neither f (v) nor f ′(v) exists where the denominator equals zero, namely, where 1 − 2v^2
= 0 or where v equals

EXAMPLE 8

If x ≠ 0, find f ′(x).

SOLUTION:

EXAMPLE 9

If y = tan (2x^2 + 1), find y ′.

SOLUTION: y ′ = 4x sec^2 (2x^2 + 1).

EXAMPLE 10