Questions 1,3,7,11, 15, 19, 21,23,27,31,Please show work. Thank you

SECTION 3.5 Implicit Differentiation 215 3.5 EXERCISES 1-4 (a) Find y' by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get y' 29. x2 + y? = (2x3 + 2y2 - x)?, (0.4). (cardioid) in terms of x. (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a). 1. 9x2 - y? = 1 2. 2x2 + x+ xy = 1 3. Vr+ vy = 1 4. 2 _ 1 -= 4 30. *2/3 + 12/3 = 4, (-3 3, 1), (astroid) 5-20 Find dy/dx by implicit differentiation. 5. x2 - 4xy + y2 = 4 6. 2x2 + xy - 12 = 2 37. x4+ xly ? + 13 = 5 8. x3 - xy2 + y3 = 1 9. - _ = y2 + 1 xty 10. xe' = x - y 31. 2 (x2 + y2 )2 = 25(x2 - y2). (3, 1), (lemniscate) 11. y cos x = x2 + 2 12. cos(xy) = 1 + sin y ( 13. Vxty = x4+ y4 14. e'sin x = x + xy ed : 15. edly = x - y 16. xy = Vx2 + y2 32. y" ( y2 - 4 ) = x2(x2 - 5), (0, -2), (devil's curve) 17. tan '(x y) = x + xy? 18. x sin y + y sin x = 1 19. sin(xy) = cos(x + y) 20. tan(x - y) = *21. If f(x) + x'[f(x)]' = 10 and f(1) - 2, find f' (D). 22. If g(x) + x sing(x) = x2, find g'( 33. (a) The curve with equation y' = 5x4 - x2 is called a 23-24 Regard y as the independent variable and x as the depen- kampyle of Eudoxus. Find an equation of the tangent dent variable and use implicit differentiation to find dx/dy. line to this curve at the point (1, 2). 23. xay' - xy + 2xy' = 0 24. y sec x = x tan y (b) Illustrate part (a) by graphing the curve and the tangent line on a common screen. (If your graphing device will graph implicitly defined curves, then use that capabil ity. If not, you can still graph this curve by graphing its 25-32 Use implicit differentiation to find an equation of the upper and lower halves separately.) tangent line to the curve at the given point. 34. (a) The curve with equation y' = x' + 3x2 is called the 25. y sin 2x = x cos 2y, (T/ 2, TT/ 4) Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, - 2). 26. sin( x + y) = 2x - 2y, (T, TT) (b) At what points does this curve have horizontal 27. x' - xy - y? = 1, (2, 1) (hyperbola) tangents? (c) Illustrate parts (a) and (b) by graphing the curve and the 28. x2 + 2 xy + 4y? = 12, (2, 1) (ellipse) tangent lines on a common screen