Finding a Derivative implicit differentiation. 5. x + y = 9 7. +=16 9. x - xy + y = 7 11. r'y - y = x 13. x-3xy + 2xy = 12 15. sin x + 2 cos 2y = 1 17. csc x= x(1+tan y) 19. y sin ry Finding Derivatives Implicitly and Explicitly In Exercises 21-24, (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly and show that the result is equivalent to that of part (c). 21. x + y = 64 22. 25x + 36y = 300 23. 16yx = 16 24. x + y - 4x + 6y + 9 = 0 x-49 find dy/dx by 6. -25 8. 2x + 3y = 64 10. y + yx = -2 12. xy = y + 1 14. x'y- 8xy + 3xy = 9 16. (sin x + cos my) = 2 18. cot y = x-y 20. x = sec - Finding the Slope of a Graph In Exercises 25-32, find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. 25. xy-6, (-6,-1) 27. y = 29. (x + y) =+y. (-1.1) 30, x + y = 6xy - 1. (2,3) 31. tan(x + y)-x. (0,0) 32. x cos y = 1. +49 (7,0) 26. 3xy=6, (1.2) -36 28. 4- x+36 (6.0)