HIGHER-ORDER DERIVATIVES Unit 3: Section 3 continued

Derivatives of Trig Functions  Write the basic trig functions and trig identities from the back cover of the book.

Proof:  Prove  Bonus: Prove

Ex 1: Find the Derivative  y = x – tan x  y = x sec x

Ex 2: Differentiate  Option 1: Quotient Rule  Option 2: Rewrite first

Show that both answers in Example 2 are Equivalent.

HOMEWORK  Pg 124 #39-53 odds, 61, 67, 68

AP Practice

V. Higher Order Derivative Notation DERIVATIVENOTATIONS 1 st y’f’(x) 2 nd y’’f’’(x) 3 rd y’’’f’’’(x) 4 th Nth

Ex 1: Find the Derivatives  A. If, find f’’’(x).

 B. If, find y’’.

Ex 2: Acceleration  Position → Velocity → Acceleration s(t) s’(t) = v(t) s’’(t) = v’(t) = a(t)  Because the moon has no atmosphere, a feather and a hammer can fall at the same rate. The position function of these falling objects on the moon is s(t) = -0.81t² + 2 where s(t) is height in meters and time is in seconds. What is the acceleration of the falling hammer after 3 seconds on the moon?

AP Practice

HOMEWORK  Pg 125 #83-92 odds, 101, 103 *you will need to FOIL the denominator when doing the quotient rule in order to take another derivative.