Formulas De Derivacion

Nº | Función | Derivada | Diferencial | Observaciones |
1) | Y=f1+f2+f3…fn | Y`X= F1`+F2`+F3`+….Fn` | ---------- | TODA fXfunción de X;A= cte. |
2) | Y= a | dydx=0 | ---------- | A= cte. |
3) |Y = x | dydx=1 | dy = dx | ---------- |
4) | Y= Av | dydx(Av)=Advdx | dy=A dv | A= cte; v= F(x) |
5) | Y= μv | dydxμv=μdvdx+vdydx | dμv=μdv+vdμ | μ ^v f(x) |
| Y= μvw |dydx=μvdwdx+μwdvdx+vwdμdx | ---------- | ---------- |
| Y= μv…z | dydx=(μv…)dzdx+(μ..z)dvdx+(v…z)dμdx | ---------- | ---------- |
6) | Y= kv | dydx(kv)=-kdvdxv2 | dkv= -kvv2 | k=cte. ;v=f(x) | Y= vk= 1kv |
7) | Y= μv |ddx=vdydx-μdvdxv2 | dμv= vdμ-μdvv2 | ---------- |
8) | Y= vn | ddxvn=nvn-1dvdx | dvn=nvn-1dv | n=cte.v=f(x) |
9) | Y= √v | ddx√v=dvdx2√v | dv=dv2√v | |
| Y= 3v | ddx3v=dvdx3√v2 | ---------- |---------- |
| Y= nv | ddxnv=dvdxn√vn-1 | ---------- | ---------- |
10) | Y=av | ddxav=avnaxdvdx | dav=avlnadv | ddxx3=3x2 |
| Y= ev | ddx(ev)=evdvdx | dev= evdv | v=fxe=2.71… |
11) | Y=lnv| ddx(lnv)=dvdxv | d(lnv)= dvv | v=f(x) |
12) | Y=lgv | ddx(lg v)=lgedvdxv= 1ln10dvdxv | ---------- | ---------- |
13) | Y=logav | ddx(logav )=logavdvdxv= 1lnaxdxv | ---------- | ---------- |14) | Y=sen v | ddxsen v=cosv dvdx | dsen v=cosv dv | v=fxv ϵ R;-1≤y≤1 |
15) | Y=cosv | ddxcos v=senv dvdx | dcosv = -sen v dv | v=fxv∈R-1≤y≤1 |
16) | Y=tanv | ddxtanv=sec2 v x dvdx | d(tanv)=sec2vdv | v=fx∀v∈R-nπ± π2 |
17) | Y=ctg v | ddxctgv=-csc2 v x dvdx | d(ctgv)=-csc2v dv | v∈R-nπy∈ )-∞;∞( |
18) | Y=secv | ddxsecv=secvtanv dvdx | d(secv)=secvtanv dv | v=fxv∈R-nπ± π2Y∈R--1;1 |
19) |Y=cscv | ddxCsc v=cscvctgv dvdx | ---------- | v∈R-nπ n∈ZY∈R--1;1 |
20) | Y=Arc Sen v | ddxarc Sen v= dvdx21-v2 | darc senv= dv21-v2 | v=fxy∈R-1≤v≤1 |
21) | Y=Arc Cos v | ddxarc cos v=-dvdx21-v2| darc cosv= - dv21-v2 | y=fxy∈R-1≤v≤1 |
22) | Y=Arc Tg v | ddxarc tg v=dvdx1+v2 | darc tg v= dv1+v2 | y=fxy∈)-∞;∞(-1≤v≤1 |
23) | Y=Arc Ctg | ddxarc ctg v=-dvdx1+v2 | darc ctg v= -dv1+v2 |...