Ncert Solutions for Class 11 Limits and Derivatives

Ncert Solutions for Class 11

Limits and Derivatives

• Exercise 12.1

• Exercise 12.2

• Miscellaneous Exercise

Limits and Derivatives

Miscellaneous Exercise

1. Find the derivative of the following functions from first principle:
(i) (-x)              (ii) ((-x)^{-1})                  (iii) (sin⁡(x+1))                (iv) (cos⁡(x-frac{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).

2. (x+a)

3. ((px+q)(frac{r}{x}+s)

4. ((ax+b)(cx+d)^2)

5. (frac{ax+b}{cx+d})

6. (frac{1+frac{1}{x}}{1-frac{1}{x}})

7. (frac{1}{ax^2+bx+c})

8. (frac{ax+b}{px^2+qx+r})

9. (frac{px^2+qx+r}{ax+b})

10. (frac{a}{x^4}-frac{b}{x^2}+cos⁡x)

11. (4sqrt{x}-2)

12. ((ax+b)^n)

13. ((ax+b)^n (cx+d)^m)

14. (sin⁡(x+a))

15. (cosec⁡x . cot⁡x)

16. (frac{cos⁡x}{1+sin⁡x})

17. (frac{sin⁡x+cos⁡x}{sin⁡x-cos⁡x})

18. (frac{sec⁡x-1}{sec⁡x+1})

19. (sin^n ⁡x)

20. (frac{a+b sin⁡x}{c+d cos⁡x})

21. (frac{sin⁡(x+a)}{cos⁡x})

22. (x^4 (5 sin⁡x-3 cos⁡x))

23. ((x^2+1) cos⁡x)

24. ((ax^2+sin⁡x )(p+q cos⁡x))

25. ((x+cos⁡x)(x-tan⁡x))

26. (frac{4x+5 sin⁡x}{3x+7 cos⁡x})

27. (frac{x^2 cos⁡(frac{π}{4})}{sin⁡x})

28. (frac{x}{1+tan⁡x})

29. ((x+sec⁡x)(x-tan⁡x))

30. (frac{x}{sin^n⁡})