Differentiation Rules

MATH 2431

General Formulas

1. ( ) 0d

cdx

2. ( ) ( ) ( )cf x cf x

3. ( ) ( ) ( ) ( )f g x f x g x 4. ( ) ( ) ( ) ( )f g x f x g x

5. ( ) ( ) ( ) ( ) ( ) ( )fg x f x g x g x f x 6. 2

( ) ( ) ( ) ( )( )

[ ( )]

f g x f x f x g xx

g g x

7. ( ) ( ) ( ( )) ( )f g x f g x g x 8. 1( )n nd

x nxdx

Trigonometric Functions

9. (sin ) cosd

x xdx

10. (cos ) sind

x xdx

11. 2(tan ) secd

x xdx

12. (sec ) sec tand

x x xdx

13. 2(cot ) cscd

x xdx

14. (csc ) csc cotd

x x xdx

Exponential and Logarithmic Functions

15. ( )x xd

e edx

16. ( ) lnx xd

a a adx

17. 1

(ln )d

xdx x

18. 1

(ln )d

xdx x

Inverse Trigonometric Functions

19. 12

1(sin )

1

dx

dx x 20. 1

2

1(tan )

1

dx

dx x

Hyperbolic Functions

21. (sinh ) coshd

x xdx

22. (cosh ) sinhd

x xdx