Differentiate the following functions (with respect to x)
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. If 
and 
then prove that 
.
21. If 
, find 
.
VII. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Differentiate the following functions (with respect to x)
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15. 16.
17. 18. 19.
20. If and then prove that .
21. If , find .