Calculus 1000A/B Lecture Notes - Lecture 12: Product Rule, Function Composition

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

Document Summary

Calculus 1000a, section 008, oct. 2: quiz 2 is open until 9:00 pm on thurs. Oct. 5: midterm exam is at 7 pm on friday oct. 27, students with a con ict need to contact academic counselling at their home faculty dean"s of ce, to request accommodation, more information about the midterm - to come. If g is differentiable at a and f is differentiable at b = g(a), then the composite function f (x) = f (g(x)) is differentiable at a and. F (x) = f (g(x))g (x) df dx df du du dx where u = g(x) (informally called inner function). Example. (e2x) = e2x(2x) = e2x2x = 2e2x. F (x) = (exex) = (ex) ex + ex(ex) = exex + exex = 2e2x. Examples. (sin(2x)) = cos(2x)(2x) = cos(2x)2 (cos(2x)) = sin(2x)(2x) = sin(2x)2 (tan(2x)) = (sec(2x))2(2x) = (sec(2x))22.