[symbol:funksjon] (x) = [symbol:rot] [tex](x^2 / 2) + ln x[/tex]
og
[symbol:funksjon] (x) = 1/ [symbol:rot] [tex]x^2+1[/tex]
derivasjon
Moderatorer: Aleks855, Gustav, Nebuchadnezzar, Janhaa, DennisChristensen, Emilga
Regner med at disse funksjonene skal deriveres?
[tex]f^\prime (x) = (\frac{x^2}{2} + lnx)^\prime = \underline{\underline{x + \frac1x = \frac{x^2+1}{x}}}[/tex]
[tex]f^\prime (x) = \left(\frac{1}{\sqrt{x^2+1}}\right)^\prime = \left((x^2+1)^{-\frac 12}\right)^\prime = -\frac 12 (x^2+1)^{-\frac32}\cdot2x = \underline{\underline{-x(x^2+1)^{-\frac32} = \frac {-x}{\sqrt{(x^2+1)^3}}}}[/tex]
[tex]f^\prime (x) = (\frac{x^2}{2} + lnx)^\prime = \underline{\underline{x + \frac1x = \frac{x^2+1}{x}}}[/tex]
[tex]f^\prime (x) = \left(\frac{1}{\sqrt{x^2+1}}\right)^\prime = \left((x^2+1)^{-\frac 12}\right)^\prime = -\frac 12 (x^2+1)^{-\frac32}\cdot2x = \underline{\underline{-x(x^2+1)^{-\frac32} = \frac {-x}{\sqrt{(x^2+1)^3}}}}[/tex]