y = 3 6 ( x 3 + 1 ) 2 - x 6 0 - 4x Now, using logarithmic differentiation logy = log/ 6 ( x 3 + 1)2 113 26 eux logy = + log ( 6 ( x 3 + 1)2 * 6 p - 4x Now, defferentiation do = 6 ( 2 3 + 17 2 3 / 6 ( x 3 + 1 ) 2 dre x6 4x x6 -4x 12 da y ( 12 ( x1 3 + 1 ) ( 3 x 2 ) . 2 6 (4x + 6 ( x 3 +1) ? Cause 18 ( x 3 + 1 ) 2 X (2 6 e- 4 x ) 2 = y 1 . [ 12 ( 3 x 2 ) x 6 24 7 + 6 ( x 3 + 1) ( 6 x5 (49 4 x ' exx ) 18 (x 3 + 1 ) ( x6 8247 ) * 5 [ 36 x 3 +6 (# 3 + 1) ( 6-4x) ] 18 (x3+ 1 ) *6 dy 3 6 (x 3 + 1 ) 2 36 23 + (6 x 3+6) (6-42) da *6 - 42 18 ( x 3 + 12 X 6nential functions. [If b # e logarithmic differentiation o situation where the rule does PROBLEMS 12.5 In Problems 1-12, find y' by using logarithmic differentiation. 24 1. y = (x + 1)2(x- 2)(x2+3) 2. y = (3x + 4)(8x - 1)2(3x2 + 1)4 3. y = (3x3 - 1)2(2x + 5)3 4. y = (2x2 +.1) 18x2 - 1 at 5. y = Vx+1vx - 1vx2 + 1 6. y = (2x+1)x3 +21/2x+5 2 V1 - x2 7. y = x2+ 5 1 - 2x 8. y = x +9 (2x2 + 2) 2 9. y = x2 ( 1 + x 2 ) (x+ 1)2(3x + 2) 10. y = Vx2 + 4 (x + 3)(x - 2) 3/ 6(x3 + 1)2 11. y = 2x - 1 12. y = V xbe- 4x In Problems 13-20, find y'. 13. y = 1+1 14. y = (2x) Vx 15. y = XVx 16. y = 17. y = (3x + 1) 2x 18. y = (x2 + 1)+1 19. y = 4exx3x 20. y = (Vx) 21. If y = (4x - 3)2x+1, find dy/ dx when x = 1. 22. If y = ( In x) inx, find dy/ dx when x = e. 23. Find an equation of the tangent line to y = (x+ 1)(x+ 2)2(x+3)2 at the point where x = 0