{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

211-1 Chain Rule

# 211-1 Chain Rule - Math 211 ws 1 Tutorial Program Chain...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 211 ws 1 Tutorial Program Chain Rule Examples: . . . . 3 7 d9 3 6 2 Goal: To differentlate c0mpos1te functions. 2! = W + 2) g = 7(33 + 2) ' (3m ) . . d 1 Comp051te Functlons: y = f(g(x)) or y = y : «5 i 23: i : E(5 i 2x)—% . (_2) Examples: y = (m3 + 2)7 9(90) 2 1:3 :— 2 y : (3 _ \$)—2 ﬂ : _2(3 _ x)—3 _ (_1) = w) dac y 2 m g 2 5 _ 293 Each of these could be simpliﬁed after you write the derivative. f 2 ﬂ Combinations: You will often have combinations of product, quotient 1 _2 and chain rules. y I W = (3 ‘ l“) e What is the “inside” function? Example 5 y = \$3 1 + \$4 gm) 2 3 _ a: for the product rule = 3:3 g(:r) = \/1 + 9:4 Wha»D is the woutsidew function? so f’(:r) : 3x2 but g7 is more complicated. 3 “90217—2 ac: 14—51% s0 llel+x4_Tl-4x3=i d g< > < > g < ) 2< > W Chain Rule for derivatives: = f'(g(:c)) og'(x) 3 a: (i) Differentiate the “outside” functions ﬁrst with the “inside” y’ = 3332‘ /1 + I4 __ fill function as the variable. V 1 + m (ii) Times the derivative of the “inside” function. Think of peeling off layers by differentiating until you get to the variable, 2 1/1 + x4 from the “outside” to the “inside.” Problems: Differentiate the following. Answers: 3 1) 3(2x + 29% 1) (2x + 3)E 33:2 3 2) —‘ 2) 2r +1 2 933+ 1 —8z3 1 3) — 3) <z4 + 3>3 —2\$ ,3/ 4 4) 1—\$2 )3(1_\$2)§ 5) [t2 + (1 + t)4]5 5[t2 + (1 -- t)4]4(2t + + t)3) 2\/E+ 1 6) ac —— ﬂ 6) — 4\/E an —— ﬂ 7) (3x —— 1)20 -3c 7) (6395 + 1x395 + 1)19 8) [(2132 + 1)3 + 5]4 8) 48\$(2l’2 -- U219»?2 + U3 + 513 1 3 1 2 1 _ _ _ _ 1 _ was I) 9>3<x In +332) 2\$ — 1 —24x + 23 1 — 10 — 0) (3x+4)5 ) (3x+4)6 11) Find the equation for the line tangent to y = ( :1: 1)2 at (—2, 4) 11) y : 4x + 12 ac l 12) Find the points on the curve y : m2: 1 where the tangent is parallel 12) (1, and (—1,—%) t0 the X—aXiS. ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

211-1 Chain Rule - Math 211 ws 1 Tutorial Program Chain...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online