Calculus 1000A/B Lecture Notes - Lecture 19: Product Rule, Quotient Rule

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

Document Summary

Calculus 1000a lecture 19 - section 3. 3 continued- derivatives of trigonometric. Quiz sometime next week; sample quiz and sample midterm exam to be posted. Homework: look at the derivatives of cotangent and cosecant using the process above. 74th order: 74 72+2 4(18) +2, we can use the product rule in this example. Differentiate sin x" or cos x" of any order (cid:1858)(cid:4666)(cid:1876)(cid:4667)= sin(cid:1876) n (cid:1858)(cid:4666)(cid:1876)(cid:4667) sin(cid:1876) (cid:4666)sin x(cid:4667) =cos(cid:1876) (cid:4666)cos(cid:1876)(cid:4667) = sin (cid:1876) (cid:4666) sin(cid:1876)(cid:4667) = cos (cid:1876) (cid:4666) cos(cid:1876)(cid:4667) =sin (cid:1876: (cid:2872)(cid:4666)sin(cid:1876)(cid:4667)=sin(cid:1876, (cid:2872)(cid:4666)cos(cid:1876)(cid:4667)=cos(cid:1876) Example 1: find (cid:2875)(cid:2872)(cid:4666)sin(cid:1876)(cid:4667: (cid:4666)(cid:2875)(cid:2870)+(cid:2870)(cid:4667)sin(cid:1876)= (cid:2870)(cid:4666)(cid:2872)(cid:4666)(cid:2869)(cid:2876)(cid:4667)sin(cid:1876)(cid:4667)= (cid:2870)sin(cid:1876)= sin(cid:1876) Example 2: find (cid:1877)=csc(cid:4666)+cot(cid:4667: (cid:1877) =(cid:4666)csc(cid:4667) (cid:4666)+cot(cid:4667)+(cid:4666)csc(cid:4667)(cid:4666)+cot(cid:4667) , = cot csc (cid:4666)+cot(cid:4667)+csc(cid:4666)(cid:883) (cid:4666)csc(cid:4667)(cid:2870) Example 3: find lim (cid:2868)si(cid:2924)(cid:2875) lim (cid:2868)(cid:4666)(cid:2875)(cid:4667)si(cid:2924)(cid:2875) (cid:4666)(cid:2875)(cid:4667: 7lim (cid:2868)si(cid:2924) =7(cid:4666)(cid:883)(cid:4667)=7, recall that lim (cid:2868)si(cid:2924) = 1. However, on a quiz or exam, leaving the answer like this would be acceptable (cid:2871)(cid:2873)(cid:3118) (cid:2872) The following table/information is important to memorize for quizzes and exams.