# uSsecఇపె2.5Implicit Differentiation149d (ascan2.5 ExercisesSee CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises.Famous Curves In Exercises 33-36, find theslope of the tangent line to the graph at the givenpoint.CONCEPT CHECK1. Explicit and Implicit Functions Describe thedifference between the explicit form of a function and an33. Witch of Agnesi:34. Cissoid:implicit equation. Give an example of each.(x2 4)y = 8(4 x)y2 = x32. Implicit Differentiationthe guidelines for implicit differentiation.Implicit Differentiation Explain when you have toimplicit differentiation to find a derivative.1In your own words, stateyy(2, 2)23useChain Rule How is the Chain Rule applied when(2, 1)finding dy/dx implicitly?322-2 -1Derivative In Exercises 5-20, find-2Findingdy/dx by implicit differentiation.36. Folium of Descartes:35. Bifolium:3y36xy 0(x2 y2) = 4x2y6. x2-y2255. x+297. xy5 169. x3-y2118. 2x3+3y3= 64410. xyy2x -212. Vxy = xy + 173(1, 1)211. x'y-y x14. xty 8xy+3xy2 =9ry) 213. x-32y2xy2 122-1-2X16. (sin4321TX +cOS15. sinx +2 cos 2y18. cot y-2x --y17. csC x x(1 + tan y)120. x sec -yFamous Curves In Exercises 37-42, find anequation of the tangent line to the graph at thegiven point. To print angraph, go to Math Graphs.com.19. y = sinxyandenlarged copy of theFinding DerivativesExplicitly In Exercises 31-24, (a) find twoexplicit functions by solving he cquntion fer y interms of x, (b) sketch the grapt of the cquatken andlabel the parts given by orraspondisg srxplicitfunctions, (c) differentiadhe explicit fnctions,and (d) find dy/dx implicisy and show ihat theresult is equivalent to that of park (c).Implicitly38. Circle37. Parabolaas(x+ 2)2+(y-3)2= 37(y-3)2= 4(x-5)1010(4, 4)22. 25x236y 30021. x2+ y2 6423. 16y2- 2= 16(6, 1)4x + 6y +9= 024. x2y2+14-2+ 2 46 84 6-4-2Finding the Slope of a Graph In Exercises25-32, find dy/dx by implicit differentiation. Thenfind the slope of the graph at the given point.-4-640. Astroid39. Cruciformx2/3y2/3525. xy = 6, (-6, - 1)26. 3x3y = 6, (1, 2)x2y2- 9x2-4y2 - 0x2-36x2-4927. y2x 49' (7,0)29. (x + y)3 = x3 + y, (-1, 1)30. y6xy - 1, (2, 3)28. 4y3111236 (6,0)4(8, 1)(-4, 2/3)+2 46Xx1231. tan(x+y) = x,-6-4 -2(0, 0)-4(a9)32. x COS y = 1,-12+2,34 21

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Step 1

Obtain dy/dx by implicit differentiation as follows.

Step 2

Simplify fur...

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