MATH 1007 Lecture Notes - Lecture 5: Quotient Rule, Chain Rule, Product Rule

• School: Carleton University
• Department: Mathematics
• Course: MATH 1007
• Professor: Ranjeeta Mallick

Document Summary

If you have a point ex: (1, 3) So the equaion of the tangent, in point slope form is y 3 = (3/2) (x 1) Product rule: d dx [f(x)g(x)] = f(x)g"(x) + f"(x)g(x) Quoient rule: d dx [f(x)/g(x)] = g f " fg " Soluion: g(2)=3 and g"(2) = (-4) x: g" ( x ) g( x, 1. Chain rule: d dx [g(f(x))] = [ g"(f(x)) ][ f"(x) ] If the funcion f is difereniable & h(x) = [f(x)]n (n is any real number), then: h"(x) = d dx ([f(x)])n = n[f(x)]n-1: f"(x) + lim h 0 cosx: sinh h f " ( x )=sinx (lim h 0. )+cosx( lim h 0 sinh h f " ( x )=sinx (0)+cosx( h 0 1) f " ( x )=0+1=1. ** memorize this shit and you can use it as a deiniion. Csc x: cot x sec x, tan x. = limx 0 [ (cosx - 1)/(x) ]/[ (sinx)/(x) ]