MATH 121 Lecture Notes - Lecture 4: Linearization, Brian Burres, Formula One

• School: Queen's University
• Department: Mathematics
• Course: MATH 121
• Professor: Alan Ableson

Document Summary

Unit #4 - interpreting derivatives, local linearity, newton"s method. Some problems and solutions selected or adapted from hughes-hallett calculus. Computing inverse trig derivatives: starting with the inverse property that sin(arcsin(x)) = Take the x derivative of both sides: d dx (cid:18) d. Recall: sin2( ) + cos2( ) = 1 so cos( ) = d dx arcsin(x) = Using this formula in the arcsin derivative formula, d dx arcsin(x) = 1 x2: starting with the inverse property that cos(arccos(x)) = x, nd the derivative of arccos(x). You will need to use the trig identity sin2(x) + cos2(x) = 1. Take the x derivative of both sides: d dx. 1 sin2( ) + cos2( ) = 1 sin( ) =(cid:112)1 cos2( ) so. Using this formula in the arccos derivative formula, d dx arccos(x) = But cos(arccos(x)) = x, so d dx arccos(x) = 1 x2: starting with the inverse property that tan(arctan(x)) = x, nd the derivative of arctan(x).