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Moderators: Aleks855, Gustav, Nebuchadnezzar, Janhaa, DennisChristensen, Emilga
[tex]f(x)=ln(x)^2 - ln(x^2) -3[/tex]
Bruker kjerneregel på ln(x) og [tex]x^2[/tex]
[tex]f^{\prime}(x)=2ln(x)\frac{1}{x} - \frac{1}{x^2}2x[/tex]
[tex]f^{\prime}(x)=2ln(x)\frac{1}{x} - 2\frac{1}{x}[/tex]
Bruker produktregelen
[tex]f^{\prime \prime}(x)=2\frac{1}{x}\frac{1}{x} + ln(x)(-\frac{1}{x^2} )-2(- \frac{1}{x^2})[/tex]
[tex]f^{\prime \prime}(x)=\frac{2}{x^2}- \frac{ln(x)}{x^2} +\frac{2}{x^2}[/tex]
[tex]f^{\prime \prime}(x)=\frac{4 -ln(x)}{x^2}[/tex]
Bruker kjerneregel på ln(x) og [tex]x^2[/tex]
[tex]f^{\prime}(x)=2ln(x)\frac{1}{x} - \frac{1}{x^2}2x[/tex]
[tex]f^{\prime}(x)=2ln(x)\frac{1}{x} - 2\frac{1}{x}[/tex]
Bruker produktregelen
[tex]f^{\prime \prime}(x)=2\frac{1}{x}\frac{1}{x} + ln(x)(-\frac{1}{x^2} )-2(- \frac{1}{x^2})[/tex]
[tex]f^{\prime \prime}(x)=\frac{2}{x^2}- \frac{ln(x)}{x^2} +\frac{2}{x^2}[/tex]
[tex]f^{\prime \prime}(x)=\frac{4 -ln(x)}{x^2}[/tex]
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