1. $\frac{d}{dx}[cu]=cu'$

2. $\frac{d}{dx}[u\pm v]=u'\pm v'$

3. $\frac{d}{dx}[uv]=uv'+vu'$

$\frac{d}{dx}[\frac{u}{v}]=\frac{vu'-uv'}{v^2}$

5. $\frac{d}{dx}[c]=0$

6. $\frac{d}{dx}[u^n]=nu^{n-1}u'$

7. $\frac{d}{dx}[x]=1$

8. $\frac{d}{dx}[|u|]=\frac{u}{|u|}(u'), u\neq 0$

9. $\frac{d}{dx}[\ln{u}]=\frac{u'}{u}$

10. $\frac{d}{dx}[e^u]=e^uu'$

11. $\frac{d}{dx}[\log_a{u}]=\frac{u'}{(\ln{a})u}$

12. $\frac{d}{dx}[a^u]=(\ln a)a^uu'$

13. $\frac{d}{dx}[\sin u]=(\cos u)u'$

14. $\frac{d}{dx}[\cos u]=-(\sin u)u'$

15. $\frac{d}{dx}[\tan u]=(\sec^2 u)u'$

16. $\frac{d}{dx}[\cot u]=-(\csc^2 u)u'$

17. $\frac{d}{dx}[\sec u]=(\sec u\tan u)u'$

18. $\frac{d}{dx}[\csc u]=-(\csc u\cot u)u'$

19. $\frac{d}{dx}[\arcsin u]=\frac{u'}{\sqrt{1-u^2}}$

20. $\frac{d}{dx}[\operatorname{arccos} u]=\frac{-u'}{\sqrt{1-u^2}}$

21. $\frac{d}{dx}[\operatorname{arctan} u]=\frac{u'}{1+u^2}$

22. $\frac{d}{dx}[\operatorname{arccot} u]=\frac{-u'}{1+u^2}$

23. $\frac{d}{dx}[\operatorname{arcsec} u]=\frac{u'}{|u|\sqrt{u^2-1}}$

24. $\frac{d}{dx}[\operatorname{arccsc} u]=\frac{-u'}{|u|\sqrt{u^2-1}}$

25. $\frac{d}{dx}[\sinh u]=(\cosh u)u'$

26. $\frac{d}{dx}[\cosh u]=(\sinh u)u'$

27. $\frac{d}{dx}[\tanh u]=(\operatorname{sech}^2 u)u'$

28. $\frac{d}{dx}[\coth u]=-(\operatorname{csch}^2 u)u'$

29. $\frac{d}{dx}[\operatorname{sech} u]=-(\operatorname{sech} u\tanh u)u'$

30. $\frac{d}{dx}[\operatorname{csch} u]=-(\operatorname{csch} u\coth u)u'$

31. $\frac{d}{dx}[\sinh^{-1} u]=\frac{u'}{\sqrt{u^2+1}}$

32. $\frac{d}{dx}[\cosh^{-1} u]=\frac{u'}{\sqrt{u^2-1}}$

33. $\frac{d}{dx}[\tanh^{-1} u]=\frac{u'}{1-u^2}$

34. $\frac{d}{dx}[\coth^{-1} u]=\frac{u'}{1-u^2}$

35. $\frac{d}{dx}[\operatorname{sech}^{-1} u]=\frac{-u'}{u\sqrt{1-u^2}}$

36. $\frac{d}{dx}[\operatorname{csch}^{-1} u]=\frac{-u'}{|u|\sqrt{1+u^2}}$