Basic Calculus Activity Sheet No. 6 EXAMPLE I Differentiate y = (4x + 3) . SOLUTION a. Using the product rule for derivation y = (4x +3)- X = (4x + 3) 4 ( 4x + 3) + ( 4x + 3) = (4x + 3) =(4x +3)(4) +(4x +3)(4) =16x +12 + 16x +12 = 32x + 24b. by expanding (4x + 3) y = (4x + 3) =16x3 + 24x +9 dy _216x3 + 2 24x + do dx de dx dx = 2(16x) + 24 +0 =32x + 24 c. By using the Chain Rule y =(4x + 3)? Solution: First, differentiate the "square" by using power rule for derivatives then differentiate the polynomial inside the parenthesis. This may be called "inner function." y =(4x + 3) y' =2(4x+3)2 - " (4x+3) =2(4x +3) .(4) =8(4x +3) = 32x + 24 EXAMPLE 2 Differentiate y = (6x - 4)'.. SOLUTION y = (6x - 4)' dx dy = 3( 6x -4)' dx - ( 6x -4 ) =3(6x -4)' (6) =18(6x -4)\fAnswer numbers: 1, 3, 5, 11, 15, 19, 21, 25 only. . . Show your complete solutions, just follow the examples above. MATH SELFIE A. Differentiate the following functions. 1. y=4x6 -5x3 +6 2. y= (3x + 2) 3. y= (5x -3) 4. y= (5x] - 3x + 1) 5. y= (2x7 - x+ 1 ) 6. y= (4x-2)' 7. y= (5-3x)' 8. y= (2 + x ) 9. y= (x + 2)2 10. y = (x-3)2 MATHgroupie B. Differentiate the following functions. 11. y= (2x) + 3x +4)3 12. y= (x -2x +3)3 13. y= (x-2)(3x + 1) 14. y = (5x +3) (2x -1) 15. y= V2x-1 16. y = V3x +5 17. y = V4x-2 18. y = (5x-2) (x +3) 19. y= (3x* + 2x -3) 20. y= (4x] -3.x + 2)' SMASH C. Differentiate the following functions. 21. y= (x +5x +2) 22. y= (2x -x+3) 23. = (x - 2x + 6) 24. y = V4x -5 25. y= V6-7x