Exercise miscellaneous

Find the derivative of the following functions from first principle: (i) x− (ii) 1( )x −− (iii) sin (x + 1) (iv) cos (x - π 8 ) Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(x + a ) 3. (px + q) r sx   +   4. ( )( ) ax b cx d+ +

ax b cx d + + 6. 11/11 x x + − 7. 2 ax bx c+ + 8. 2 ax b px qx r + + + 9. 2px qx r ax b + + + 10. 4 2 cosa b x x x − + 11. 4 2x − 12. ( ) nax b+ 13. ( ) ( ) n max b cx d+ + 14. sin (x + a) 15. cosec x cot x 16. cos 1 sin x x+ 17. sin cos sin cos x x x x + − 18. sec 1 sec 1 x x − + 19. sin n x 20. sin cos

• / + 21. sin( ) / cos / x a x + 22. 4 (5sin 3cos )x x x − 23. ( ) 2 1 cosx x+ 24. ( )( )2 sin cosax x p q x+ + 25. ( ) ( )cos tanx x x x+ − 26. 4 5sin 3 7cos x x x x + + 27. 2 cos 4 sin x x π     28. 1 tan x x+ 29. ( ) ( )sec tanx x x x+ − 30. sinn x x