Matematicas

Reglas de Derivación
Sean u = f(x), v = g(x) y w = h(x) funciones diferenciables de x. Sean además, c y n números reales(c, n 2 R) y a una constante real positiva (a 2 R+).
1. d(c) = 0
dx

2. d (x) = 1
dx

3. d (xn) = nxn-1
dx

4. d (cu) = c du
dx dx

5. d (u ± v ± w) = du ± dv ± dw
dxdx dx dx

6. d (ex) = ex
dx

7. d (uv) = u dv + v du
dx dx dx

8. d ( u.v ) = v du − u dv
dx dxdx
v2
9. d (sin x) = cos x
dx

10. d (cos x) = −sin x
dx

11. d (tan x) = sec2 x
dx

12. d (csc x) = −csc x cotx
dx

13. d (sec x) = sec x tan x
dx

14. d (cot x) = −csc2 x
dx

15. (Regla de la Cadena) Sea y = f(u),
dy = dy. du
dx du dx

16. d (un)= nun-1 du
dx dx

17. d (eu) = eu du
dx dx

18. d (sin u) = cos u du
dx dx

19. d(cos u) = −sin u du
dx dx

20. d (tan u) = sec2 u du
dx dx

21. d (csc u) = −csc u cot u du
dxdx

22. d (sec u) = sec u tan u du
dx dx

23. d (cot u) = −csc2 u du
dxdx

24. d (ax) = ax ln a
dx

25. d
dx (sin−1 x) = p 1
1−x2
26. d
dx (cos−1 x) = −p 1
1−x2
27. d
dx (tan−1 x) = 1
1+x2
28. d
dx (csc−1 x) = − 1x
p
x2−1
29. d
dx (sec−1 x) = 1
x
p
x2−1
30. d
dx (cot−1 x) = − 1
1+x2
31. d
dx (loga x) = 1
x ln a
32. d
dx (ln x) = 1
x
33. d
dx (ln u) = 1
u · du
dx
Calculo