Matematicas
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
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