Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x) tany = Vu2 - 1 and u> 010:23(ii) if0Thus, tany**Vu? - 1,u<0From (*) and (* *), we haveProf. Dr. Raad Salih MahdiCollege of Oil and Gas Engineeringu >0uvu2-1dy1%3DduJulVu?-1u<0uvu2-1dyHence from (#),1dudui.e., axJulVu?-1 dx'sec-lu =%3DI21 dxExercise (6.2)Prove the remaine itonExamples (6.3)Find y' for the following:theorem (6.1).(1) y = sin-(cos/x) + cos-(sin/x)1V1-cos-Vx2 a)V1-sin?V (coSyx. ).(-sinvx. )(cosv. )1%3DVsin?Vx2 vxVcos?Vx2.(-sinvx. )-(cosv. )%3D|sinvx|2 vx)cosvx2 Vx)-11+(x+y)2(1+y') =1+(xy)?(xy' + y)1-xy'y1+(xy)?%3D1+(x+y)21+(x+y)2Y1+(xy)?ху1+(xy)2y1y' +1+(x+y)21+(xy)21+(x+y)2y1->1+(xy)2]1+(xy)21+(x+y)2sinva2 vx. |sinvA 2 vx.|cosvx|1+(xy)21+(x+y)2cosvxy' =l1+(x•1+(xy)²(2) tan-1(x + y) = 4 + cot-(xy)Prof. Dr. Raad Salih MahdiCollege of Oil and Gas EngineeringSol.Example (6.4)Let y = tanr. Show thatرغدة(1+x2)?y" + 2x(1 + x²)y' + y + cot-lx =.29.03.21 at 10:22 AM1+x(1+x2)2

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Math

Algebra

Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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