MATH 1190 Lecture Notes - Lecture 10: Product Rule

• School: KSU
• Department: Mathematics
• Course: MATH 1190
• Professor: Vandenbussche, Jennifer

Document Summary

Math 1190: section 3. 1 the chain rule, consider: f(x) = sin( ) a. i. Can be broken into: f(x) = h(g(x)) or h g a. i. 1. Where: h(x) = sin(x) & g(x) : chain rule b. i. If f and g are differentiable b. i. 1. b. i. 2. Then: (f g) = f (g(x)) g (x) Note: f is the outside equation and g is the inside equation b. ii. Example #1 b. ii. 1. f(x) = sin( ) b. ii. 1. a. f = sin(x) b. ii. 1. b. g = b. ii. 1. c. (f g) = f (g(x)) g (x) b. ii. 1. d. Example #2 b. iii. 1. f(x) = b. iii. 1. a. f = b. iii. 1. b. g = b. iii. 1. c. Note: y = is the same as y = b. iv. 1. b. f = b. iv. 1. c. g = tan(x) b. iv. 1. d. Chun 2 b. v. 1. y = csc (cos(x)) b. v. 1. a. f = csc(x) b. v. 1. b. g = cos(x) b. v. 1. b. i. Csc(cos(x)) cot(x) cos(x) - sin(x) b. v. 1. b. ii. sin(x) csc(cos(x)) cot(cos(x)) b. vi.