Differentiation Formulas This page contains a list of commonly used differentiation formulas. x1. Derivative of a Constant (k):

[ ] 0d kdx

= 2. Constant-Multiple Rule:

[ ]( ) '( )d k f x k f xdx

= 3. Sum/Difference Rule:

[ ( ) ( )] '( ) '( )d f x g x f x g xdx

= 4. Power Rule:

1r rd x rxdx

= 5. Product Rule:

[ ( ) ( )] ( ) '( ) ( ) '( )d f x g x f x g x g x f xdx

= + 6. Quotient Rule:

[ ]2( ) '( ) ( ) '( ) ( )( ) ( )

d f x f x g x g x f xdx g x g x

= 7. Reciprocal Rule:

21 ' ( ) [ ( )]

d gdx g x g x

= ( )x

8. Chain Rule:

( ) ( )( ) ' ( ) '( )d f g x f g x g xdx

=

9. xd e edx

=

10. [ ] 1ln( ) ( 0)d x xdx x

= >

11. lnx xd a a adx

=

12. [ ] 1loglna

d xdx x a

=

13. [ ]sin cosd x xdx

=

14. [ ]cos sind x xdx

=

15. [ ] 2tan secd x xdx

=

16. [ ]sec sec tand x x xdx

=

17. [ ]csc csc cotd x x xdx

=

18. [ ] 2cot cscd x xdx

=

19. 12

1sin1

d xdx

= x20. 1 2

1tan1

d xdx x

= +21. 1

2

1sec1

d xdx x x

=

22. 12

1cos1

d xdx

= x23. 1 2

1cot1

d xdx x

= +

24. 1cscd xdx

= 21

1x x

revised 12/07