Warmup If () = 5 4 means  ′ () = 20 3 , then what is lim ℎ→0 5(3 + ℎ) 4 − 5(3 4 ) ℎ fq x f G lismf dd x 7 17 16 O f 421 17.216 O f 3 f 3 20.33 5406 Chapter 3 – Short-cuts to Differentiation 3.1 – Powers and Polynomials Review rules/short-cuts l

Warmup for 4.1.1 – do this on the board 1. If 3 2 + 2 +  2 = 2, then the value of   at =1 is A. −2 B. 0 C. 2 D. 4 E. not defined Warmup for 4.1.2 – do this on the board 2. Let  be the function given by () =  3 − 3 2 . What are all value

Warmup 1. Solve the initial value problem.   = 4  a. Condition: When  = 0,  = 4 b. Condition: When  = 0,  = −6 dy x4ydx ft ydy fx.dk a h 4 te h 4 c butyl to µ yl 5th4 x5 5 1C x th4 lyl e lyl e y1 e e ly e eh4 y e ec Let K Iec 1yl e 4 g K e

Warmup 1. Given  = arctan( 2   ) determine   . 2. If ℎ() = ( () ) 4 determine ℎ ′ (3) given (3) = 2 and  ′ (3) = 5. 4 h X 4 f f x h 3 4G GD f 3 CT 4 2 3 5 20 8 We will know: Implicit functions We will understand: Shortcuts, when they are

Warmup Find the derivative function. Note: number 1 is easy enough to simplify after you have taken the derivative, but do not worry about trying to simplify number 2 1.  = 2  (3 5 − 4 2 ) 2. () =  2 + 5   + 3 d dd 2 3 5 4 2 12 1,13 5.4 2