Table of Derivatives
( \newcommand{\kernel}{\mathrm{null}\,}\)
General Formulas
1. ddx(c)=0
2. ddx(f(x)+g(x))=f′(x)+g′(x)
3. ddx(f(x)g(x))=f′(x)g(x)+f(x)g′(x)
4. ddx(xn)=nxn−1,for real numbers n
5. ddx(cf(x))=cf′(x)
6. ddx(f(x)−g(x))=f′(x)−g′(x)
7. ddx(f(x)g(x))=g(x)f′(x)−f(x)g′(x)(g(x))2
8. ddx[f(g(x))]=f′(g(x))·g′(x)
Trigonometric Functions
9. ddx(sinx)=cosx
10. ddx(tanx)=sec2x
11. ddx(secx)=secxtanx
12. ddx(cosx)=−sinx
13. ddx(cotx)=−csc2x
14. ddx(cscx)=−cscxcotx
Inverse Trigonometric Functions
15. ddx(arcsinx)=1√1−x2
16. ddx(arctanx)=11+x2
17. ddx(arcsecx)=1|x|√x2−1
18. ddx(arccosx)=−1√1−x2
19. ddx(arccotx)=−11+x2
20. ddx(arccscx)=−1|x|√x2−1
Exponential and Logarithmic Functions
21. ddx(ex)=ex
22. ddx(ln|x|)=1x
23. ddx(bx)=bxlnb
24. ddx(logbx)=1xlnb
Hyperbolic Functions
25. ddx(sinhx)=coshx
26. ddx(tanhx)=sech2x
27. ddx(sechx)=−sechxtanhx
28. ddx(coshx)=sinhx
29. ddx(cothx)=−csch2x
30. ddx(cschx)=−cschxcothx
Inverse Hyperbolic Functions
31. ddx(arcsinhx)=1√x2+1
32. ddx(arctanhx)=11−x2(|x|<1)
33. ddx(arcsechx)=−1x√1−x2(0<x<1)
34. ddx(arccoshx)=1√x2−1(x>1)
35. ddx(arccothx)=11−x2(|x|>1)
36. ddx(arccschx)=−1|x|√1+x2(x≠0)
Contributors
Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
- Modified to change inverse trig notation by Paul Seeburger (Monroe Community College)