Calculus 1000A/B Lecture Notes - Lecture 13: Chain Rule, Implicit Function, Inverse Trigonometric Functions

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Pei Yu

Document Summary

Chain rule warm-up examples: (cid:16)(sin x)3(cid:17) = 3(sin x)3 1(sin x) = 3(sin x)2 cos x (sin(x3)) = cos(x3)(x3) = cos(x3)3x2. A new useful fact: for a positive constant a. 5x + 1(cid:17) = (x2) (5x + 1) x2(5x + 1) (5x + 1)2. 2x(5x + 1) x2(5x ln 5 + 0) (5x + 1)2. If the tangent line to the graph of the function f (x) = 3x c has slope ln 27 when x = 3, nd the value of c. If the tangent line to the graph of the function f (x) = 3x c has slope ln 27 when x = 3, nd the value of c. ln 27 = f (3) = (3x c) (cid:12)(cid:12)(cid:12)x=3. = 3x c ln 3(x c) (cid:12)(cid:12)(cid:12)x=3 ln 27 = 33 c ln 3. = 3x c ln 3(1 0)(cid:12)(cid:12)(cid:12)x=3 ln(33) = 33 c ln 3. 1 = 3 c = c = 2.