770
Appendix B
⎛ ⎝ cos −1 x
⎞ ⎠ = − 1
18. d
dx
1− x 2
⎛ ⎝ cot −1 x
⎞ ⎠ = − 1
19. d
dx
1+ x 2
⎛ ⎝ csc −1 x
⎞ ⎠ = − 1
20. d
dx
| x | x 2 −1 Exponential and Logarithmic Functions 21. d dx ( e x ) = e x 22. d dx (ln| x |) = 1 x 23. d dx ( b x ) = b x ln b 24. d dx ⎛ ⎝ log b x ⎞ ⎠ = 1 x ln b Hyperbolic Functions 25. d dx (sinh x ) =cosh x 26. d dx (tanh x ) = sech 2 x 27. d dx (sech x ) =−sech x tanh x 28. d dx (cosh x ) = sinh x 29. d dx (coth x ) =−csch 2 x 30. d dx (csch x ) =−csch x coth x Inverse Hyperbolic Functions 31. d dx ⎛ ⎝ sinh −1 x ⎞ ⎠ = 1 x 2 +1 32. d dx ⎛ ⎝ tanh −1 x ⎞ ⎠ = 1 1− x 2 (| x | <1) 33. d dx ⎛ ⎝ sech −1 x ⎞ ⎠ = − 1 x 1− x 2 (0< x <1) 34. d dx ⎛ ⎝ cosh −1 x ⎞ ⎠ = 1 x 2 −1 ( x >1) 35. d dx ⎛ ⎝ coth −1 x ⎞ ⎠ = 1 1− x 2 (| x | >1) 36. d dx ⎛ ⎝ csch −1 x ⎞ ⎠ = − 1 | x | 1+ x 2 ( x ≠0)
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online