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deriver

f (x) = ln ( √ x )

janneamble wrote:deriver

f (x) = ln ( √ x )

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u = [symbol:rot] (X)


[tex]{d\over dx}ln(u)\;=\;[/tex][tex]u `\over u[/tex]

[tex](ln\sqrt {x})`\;=\;[/tex][tex]0.5x^{-0.5}\over x^{0.5}[/tex]

[tex](ln\sqrt {x})`\;=\;[/tex][tex]0.5x^{-1}[/tex]

[tex](ln\sqrt {x})`\;=\;[/tex][tex]1\over {2}{x}[/tex]

Du kan også benytte deg av at [tex] \ln (\sqrt{x}) = \frac{1}{2} \ln (x)[/tex]

[tex]\frac{d}{dx} \ \frac{1}{2} \ln (x) = \frac{1}{2x}[/tex]