1. (f + g) (x) = f (x) + g (x)
2. (a · f) (x) = af (x), gdzie a - staÅ‚a
3. (f · g) (x) = f (x)g(x) + f(x)g (x)

f f (x)g(x)-f(x)g (x)
4. (x) =
g (g(x))2
5. (g ć% f) (x) = g (f(x)) · f (x)
6. a = 0, gdzie a - stała
7. (xn) = nxn-1, dla n " R
"
1
"
8. ( x) =
2 x
1 1
9. (x) = -
2
x
10. (sin x) = cos x
11. (cos x) = - sin x
1
12. (tg x) =
cos2 x
1
13. (ctg x) = -
sin2 x
1
"
14. (arc sin x) =
1-x2
1
"
15. (arc cos x) = -
1-x2
1
16. (arc tg x) =
1+x2
1
17. (arc ctg x) = -
1+x2
18. (ex) = ex
19. (ax) = ax ln a, dla a > 0
1
20. (ln x) =
x
1
21. (loga x) = , dla a > 0, a = 1

x ln a