Mathematics 0110A/B Study Guide - Quiz Guide: Quotient Rule

• School: Western University
• Department: Mathematics
• Course: Mathematics 0110A/B
• Professor: Chris Brandl

Document Summary

Assignment 6 solutions: compute the indicated derivatives for the following functions. (a) f (x) = 2 x (cid:17) (cid:0)6 + 2 (cid:16) x2 )(x2 + 2: (6x 2 (x2 + x (cid:17) (cid:16) x)2. 12x2 4 + 3 x)2 x 1. 2 x sin ( x)(sin (x)) cos ( : cos (x) (sin (x))2, find f(cid:48)(x) (a) f (x) = x arctan(sin (x3)) f(cid:48)(x) = x 1arctan(sin (x3)) + x 3x2 cos (x3) 1 (cid:18) 1 (cid:19)ln(x) x (b) f (x) = We will use logarithmic di erentiation to nd the indicated derivative. We rst take the logarithm of both sides of the equation and simplify. y = ln (y) = ln x (cid:19)ln(x) (cid:18) 1 (cid:19)ln(x)(cid:33) (cid:32)(cid:18) 1 (cid:18) 1 (cid:19) x. = 2 ln (x) y(cid:48) y y(cid:48) = 2 ln (x) x x. = 2 ln (x) x y (cid:19)ln(x) (cid:18) 1 (cid:19)ln(x) (cid:18) 1 x.