Directions:

Answer the following and show solutions.

(please see photos for reference)

3.5 Implicit Differentiation 131 3.5 SUPPLEMENTARY PROBLEMS In Prob. 1-22, find dy/dx, if 1. x2 - x+ y' = 2xy 2. 3x2 + 12 = 4xy 3. x2 - y2 + xy = x2y 4. 5x2 - xy - 4y2 = 0 5. x2 + 2xy + 12 = 0 6. x2 + y2 - 4ax2 = 1 7. x3 + yz = 3+ xy 8. y' + x3 + 12 = x 9. x2 + yz = 2a xy + - X 2 11. ty = xy 12. (y - a) +x2 = b 13. J x + y = xy 14. x3 + y' - 3axy =0 15. x+ y+(xy) = 1 16. y- a =x+y2 17. yz = 1 18. x2 yz a2 62 = 1 19. 4x2 - 9y2 -x+y =1 20. 4x2 + y2 + x+ y= 0 21. y +x2y = x2+2 22. 1 +2x2 +y = x In Prob. 23-30, find day dx2 at the indicated value of x and y. 23. xy? = 2- x3y; at x = 1, y=2. 24. x2 + y? = 3 + xy; at x = 1, y=-1. 25. y2 = 3xy - x3; at x = 1, y = 1 26. y2 = 2xy + 3; at x = 1, y =3 27. x2 + y? = 2xy + 4x; at x =1, y =3 28. y = 2 -(xy) ; atx = 1, y=-2 29. (xy)3 - 8 =0; at x = 2, y = 1 30. (x -2)y = 1 - 2xy + x; at x = 4, y = 2Exercises . find the derivative of the function. f ( * ) = 3 sin x Compute the derivative. 2. 9( x ) = sinx + cos x 15. Dy ( cot y csc y) 27. De 2 eset - 1 iset+ 2 3 . g ( x ) = tanx + cotx 14. Dx ( ces x cot x) 28 . Ry tan y +? tany 4. f ( x ) = 4 5ecx - 2 ege x 17. D2( 2+1 5. 4(+) = at cost 18. DE Sin 6. f ( * ) = 4 x7 605 x 19 . Sin X 7. 9 (x ) = * 5in x+ 605 x 1 - Gas x 8. 9 ( y) = 3 sin y - y cos y 20 . x+4 212 6OS X 9. h(x ) = 4 six cs x tant 21. Cost - 4 10. gly) . 35 x sinx + 2x Cos x 22 . $ 12 11. f ( x ) = x cos x - 2x sinx - 2 cos x 12 . " ( y) = y -y cosy + zysing + 2 cosy 13 . sin x - 13. f ( x ) = 3 sec x tan x 24 . Cos * + 1 14. f ( t ) = sint tant 25 . Rx / ( x - sin * )(* + cos x ) ] 26. Da [ (2" + Cos 2) (az - sin 2)]