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. \(4\sqrt{x}-2\)

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. \(\frac{x}{sin^n⁡}\)