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**Miscellaneous Exercise**

**1. Find the derivative of following functions from first principle:**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**Ans. (i)**Given: then

= = =

**(ii)**Given:

then

= = =

**(iii)**Given:

then

=

= =

**(iv)**Given:

then

=

=

=

**Find the derivative of the following functions (it is to be understood that and are fixed non-zero constants and and are integers).**

**2. **

**Ans. **Given:

= 1

**3. **

**Ans. **Given:

=

= =

**4. **

**Ans. **Given:

=

**5. **

**Ans. **Given:

= =

**6. **

**Ans. **Given:

=

= =

**7. **

**Ans. **Given:

=

**8. **

**Ans. **Given:

**9. **

**Ans. **Given:

**10. **

**Ans. **Given:

=

**11. **

**Ans. **Given:

=

**12. **

**Ans. **Given:

= =

**13. **

**Ans. **Given:

**14. **

**Ans. **Given:

=

**15. **

**Ans. **Given:

=

**16. **

**Ans. **Given:

= =

=

**17. **

**Ans. **Given:

**18. **

**Ans. **Given:

**19. **

**Ans. **Given:

=

**20. **

**Ans. **Given:

=

**21. **

**Ans. **Given:

= =

**22. **

**Ans. **Given:

**23. **

**Ans. **Given:

=

**24. **

**Ans. **Given:

**25. **

**Ans. **Given:

**26. **

**Ans. **Given:

**27. **

**Ans. **Given:

=

**28. **

**Ans. **Given:

=

**29. **

**Ans. **Given:

**30. **

**Ans. **Given:

=

=

=