Formulación matemática

Fórmulas de Diferenciación.
1.− dc=0
2.− dx=dx
3.− dxn=nxn−1dx
4.− d (cu)=cdu
5.− d (u+v−w)=du+dv−dw
6.− d (un)=nun−1du
7.− d (uv)=udv+vdu
8.− d (uvw)=uvdw+uwdv+vwdu
9.− d (u/v)=vdu−udv/v2
10.− d (u/c)=du/c =1/c du
11.− d (c/v)= − cdv/v2
12.− d sen v= cos vdv
13.− d cos v= − sen vdv
14.− d tan v = sen2 vdv
15.− d cot v = − csc2 vdv
16.− d In v= dv/v = 1/v dv
17.− d Log v= Log e dv/v
18.− d ev=evdv
19.− d av = Ln a avdv
20.− duv = v uv−1 du+uvLn udv
21.− d Arc Sen v = dv / 2
22.− d Arc Tan V = dv / v2+1
23.− d Arc Cos V = − dv/ 2
24.− d Arc Cot V = − dv/ v2+1
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25.− d Arc Sec V = du / v
26.− d Arc Csc V = − dv / v
27.− d = du / 2
28.− d
=
Identidades Trigonométricas.
1.− Sen x Csc x = 1 Sen x= 1 / Csc x ; Csc x = 1 / Sen x
2.− Cos x Sen x= 1 Cos x= 1 / Sen x ; Sen x = 1 / Cos x
3.− Tan x Cot x = 1 Tan x= 1 / Cot x ; Cot x = 1 / Tan x
4.− Tan x = Sen x / Cos x
5.− Cot x = Cos x / Sen x
6.− Sen2x + Cos2x = 1 Sen2x = 1 − Cos2x ; Cos2x = 1− Sen2x
7.− Sec2x = Tan2x + 1
8.− Tan2x = Sec2x − 1
9.− Csc2x = Cot2x + 1
10.− Cot2x = Csc2x − 1
11.− Sen2x = 2Sen x Cos x
12.− Cos2x = Cos2x − Sen2x
13.− Sen2x =
−
Cos2x
14.− Cos2x =
+
Cos2x
15.− Sen (x+y) = Sen x Cos y + Sen y Cos x
16.− Sen (x−y) = Sen x Cos y − Sen y Cos x
17.− Cos (x+y) = Cos x Sen y − Sen x Sen y
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18.− Cos (x−y) = Cos x Cos y + Sen x Sen y
19.− Sen x Cos y =
Sen (x−y) +
Sen (x+y)
20.− Cos x Cos y =
Cos(x−y) +
Cos(x+y)
21.− Sen x Sen y =
Cos(x−y) −
Cos (x+y)
Formulas de Integración
1.− " dx = x + c
2.− " xndx = xn−1 + c ; n " − 1
3.− " k du = k " du
4.− " (du + dv + dw) = " du + " dv − " dw
5.− " undu= (un−1 / n+1) + c ; n " −1
6.− " dv / v = Ln v +c
7.− " ev dv = ev + c
8.− " av dv = (1 / Ln a) av + c
9.− " du = 2/3 3 + c
10.− " dx = 2/3 3 + c
11.− " Sen u dv = − Cos v + c
12.− " Cos v dv = Sen v + c
13.− " Sec2 v dv = Tan v + c
14.− " Csc2 v dv = − Cot v +c
15.− " Sen v Tan v dv = Sen v + c
16.− " Csc v Cot v dv = − Cos v + c
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17.− " Tan v dv = Ln Sec v + c = − Ln Cos v + c
18.− " Cot v dv = Ln Sen v + c = − Ln Csc v + c
19.− " Sec v dv = Ln |Sec v + Tan v| + c
20.− " Csc v dv = Ln |Csc v − Cot v| + c
21.− " dv/v2 + a2 = Arc Tan + c
22.− " dv / v2 − a2 = Ln | | + c
23.− " dv / a2 − v2 = Ln | | + c
24.− " dv /
= Arc Sen + c
25.− " dv / = Ln | v + | + c
26.− " dv / = Arc Sen + c
27.− " dv = + Arc Sen + c
28.− " dv =
Ln | v +
|+c
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