Definicija diferencijala i tablični izovodi (diferencijali)

Funkcija

[latex]\displaystyle\,f:(a,b)\subseteq\,R\rightarrow\,R[/latex]

je diferencijabilna u tački [latex]x_0\in (a,b)[/latex]

ako postoji granična vrednost (koja se naziva izvod):

[latex size=”1″]\lim\limits_{x \to \infty}\frac{f(x)-f(x_0)}{x-x_0}[/latex]

Alternativna oznaka

[latex size=”1″]f'(x_0)=\frac{d}{dx}f(x_0)=\frac{df}{dx}|_{x=x_0}[/latex]

Tablica izvoda elementarnih funkcija

Tablica izvoda elementarnih funkcija
funkcija izvod
[latex size=”1″]c\,(constant)[/latex] [latex]0[/latex]
[latex size=”1″ background:”f5f5f5″]x[/latex] [latex size=”1″ background=”f5f5f5″]1[/latex]
[latex size=”1″]ax+b[/latex] [latex size=”1″]a[/latex]
[latex size=”1″ background=”f5f5f5″]x^2[/latex] [latex size=”1″ background=”f5f5f5″]2x[/latex]
[latex size=”1″]x^3[/latex] [latex size=”1″]3x^2[/latex]
[latex size=”1″ background=”f5f5f5″]{1 \over x}[/latex] [latex size=”1″ background=”f5f5f5″]-\frac{1}{x^2}[/latex]
[latex size=”1″]x^n[/latex] [latex size=”1″]nx^{n-1}[/latex]
[latex size=”1″ background=”f5f5f5″]\frac{a}{ax+b}[/latex] [latex size=”1″ background=”f5f5f5″]\frac{-a}{ax+b^2}[/latex]
[latex size=”1″]\frac{1}{x^2}[/latex] [latex size=”1″]-\frac{2}{x^3}[/latex]
[latex size=”1″ background=”f5f5f5″]\frac{1}{x^3}[/latex] [latex size=”1″ background=”f5f5f5″]-\frac{3}{x^4}[/latex]
[latex size=”1″]\frac{1}{x^n}[/latex] [latex size=”1″]-\frac{1}{x^{n+1}}[/latex]
[latex size=”1″ background=”f5f5f5″]\sqrt{x}[/latex] [latex size=”1″ background=”f5f5f5″]\frac{1}{2\sqrt{x}}[/latex]
[latex size=”1″]\sqrt{ax+b}[/latex] [latex size=”1″]\frac{a}{2\sqrt{ax+b}}[/latex]
[latex size=”1″ background=”f5f5f5″]\frac{ax}{\sqrt{ax^2+b}}[/latex] [latex size=”1″ background=”f5f5f5″]\frac{ax}{\sqrt{ax^2+b}}[/latex]
[latex size=”1″]\sqrt{r^2-x^2}[/latex] [latex size=”1″]-\frac{x}{\sqrt{r^2-x^2}}[/latex]
[latex size=”1″ background=”f5f5f5″]e^x[/latex] [latex size=”1″ background=”f5f5f5″]e^x[/latex]
[latex size=”1″]a^x[/latex] [latex size=”1″]a^xlna[/latex]
[latex size=”1″ background=”f5f5f5″]lnx[/latex] [latex size=”1″ background=”f5f5f5″]\frac{1}{x}[/latex]
[latex size=”1″]log_ax[/latex] [latex size=”1″]\frac{1}{xlna}=\frac{1}{x}log_ae[/latex]
[latex size=”1″ background=”f5f5f5″]lnf(x)[/latex] [latex size=”1″ background=”f5f5f5″]\frac{f'(x)}{f(x)}[/latex]
[latex size=”1″](f(x))^2[/latex] [latex size=”1″]2f(x)f'(x)[/latex]
[latex size=”1″ background=”f5f5f5″](f(x))^n[/latex] [latex size=”1″ background=”f5f5f5″]n(f(x))^{n-1}f'(x)[/latex]
[latex size=”1″]\sqrt[n]{x}[/latex] [latex size=”1″]\frac{1}3\sqrt[3]{x^2}[/latex]
[latex size=”1″ background=”f5f5f5″]\sqrt[n]{x}[/latex] [latex size=”1″ background=”f5f5f5″]\frac{1}{n\sqrt[n]{x^{n-1}}}[/latex]
[latex size=”1″]sin\,x[/latex] [latex size=”1″]cos\,x[/latex]
[latex size=”1″ background=”f5f5f5″]cos\,x[/latex] [latex size=”1″ background=”f5f5f5″]-sin\,x[/latex]
[latex size=”1″]tg\,x[/latex] [latex size=”1″]\frac{1}{cos^2x}[/latex]
[latex size=”1″ background=”f5f5f5″]ctg\,x[/latex] [latex size=”1″ background=”f5f5f5″]-\frac{1}{sin^2x}[/latex]
[latex size=”1″]sec\,x[/latex] [latex size=”1″]\frac{sin\,x}{cos^2x}[/latex]
[latex size=”1″ background=”f5f5f5″]cosec\,x[/latex] [latex size=”1″ background=”f5f5f5″]-\frac{cos\,x}{sin^2x}[/latex]
[latex size=”1″]arcsin\,x[/latex] [latex size=”1″]\frac{1}{\sqrt{1-x^2}}[/latex]
[latex size=”1″ background=”f5f5f5″]arccos\,x[/latex] [latex size=”1″ background=”f5f5f5″]\frac{-1}{\sqrt{1-x^2}}[/latex]
[latex size=”1″]arctg\,x[/latex] [latex size=”1″]\frac{1}{1+x^2}[/latex]
[latex size=”1″ background=”f5f5f5″]arcctg\,x[/latex] [latex size=”1″ background=”f5f5f5″]\frac{1}{1+x^2}[/latex]
[latex size=”1″]arcsec\,x[/latex] [latex size=”1″]\frac{1}{x\sqrt{x^2-1}}[/latex]
[latex size=”1″ background=”f5f5f5″]arccosec\,x[/latex] [latex size=”1″ background=”f5f5f5″]\frac{-1}{x\sqrt{x^2-1}}[/latex]

6 thoughts on “Definicija diferencijala i tablični izovodi (diferencijali)

  1. Tablicni izvodi nastaju racunanjem izvoda po definiciji. Svaki izvod moze da se racuna tako sto se u limes koji predstavlja definiciju izvoda zameni funkcija (samo sto se to onda cesce koristi oblik limesa u kom se uzima h =X-Xo). Ovo za slozene funkcije moze da bude izuzetno komplikovano, p a se u pra ksi koriste tablicni izvodi.

    • Dali postoji literatura koja se bavi dokazivanjem tablicnih izvoda i integrala. Jedan deo ja potpuno razumem ali bih voleo da to prosirim koliko to budem mogao,Nevolim da neke formule koristim zdravo za gotovo i da ih pamtim na pamet ako mogu da se izvedu po potrebi. (e^x ; a^x ; lnx ; logaritamski i trigonometrijski).Izvini ako gnjavim sa ovi ali bih voleo ovo da razjasnim.
      POZDRAV!!!!

  2. Rapala Fishing Daily Catch tricks is the best device we have ever build up for producing boundless Gold and Silver specifically in your smartphone without squandering cash to purchase the asset, basic recovery and simple to utilize. besides it won’t have to Jailbreak or Root your gadget for getting the asset and works superbly in every Android and Ios stage gadget nevertheless off kilter that you obsession to focus of this amusement necessity goal first. Rapala Fishing Daily Catch cheats apparatus likewise have sharp to boycott framework in the considering it outfitted taking into consideration 256-Bit encryption which ensured the client and ensure that it has a most extreme succession next-door to we save going upon it ordinary appropriately it generally be fine taking into account any diversion rendition and any gadget stage. In extra word this apparatus is in view of that intense in creating Gold and Silver like free, quick and 100% secure for your record. Here is the primary behavior elements of this instrument:resolved Gold, total Silver, Unlock all level, no Root/Jailbreak required, counter to Ban (When overhaul to a more going on to date form) and Cheats likewise works culminate just on Android and Ios platforms device follow this link for more info

  3. Rapala Fishing Daily Catch tricks is the best device we have ever build stirring for producing boundless Gold and Silver specifically in your smartphone without squandering cash to buy the asset, basic recovery and easy to utilize. moreover it won’t have to Jailbreak or Root your gadget for getting the asset and works superbly in all Android and Ios stage gadget nevertheless off kilter that you obsession to focus of this amusement necessity want first. Rapala Fishing Daily Catch cheats apparatus likewise have harsh to boycott framework in the considering it outfitted taking into consideration 256-Bit encryption which ensured the client and ensure that it has a most extreme taking over next to we save going on it everyday appropriately it generally be good taking into account any diversion rendition and any gadget stage. In supplementary word this apparatus is in view of that intense in creating Gold and Silver taking into consideration free, quick and 100% safe for your record. Here is the primary tricks elements of this instrument:unadulterated Gold, sum Silver, Unlock all level, no Root/Jailbreak required, counter to Ban (When overhaul to a more happening to date form) and Cheats likewise works culminate just on Android and Ios platforms device follow this link for more info

Leave a Reply

Your email address will not be published. Required fields are marked *