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oppgave:

vis at ( lg x )` = 1 / x ln 10

janneamble wrote:oppgave:

vis at ( lg x )` = 1 / x ln 10

[tex]VET:[/tex]

[tex]{log_a(x)}\;=\;[/tex][tex]ln(x)\over ln(a)[/tex]

vel deriver i vei:

[tex]{d\over dx}[{log_a(x)}]\;=\;[/tex][tex]{d\over dx}[{ln(x)\over ln(a)}][/tex][tex]\;=\;{1\over xln(a)}[/tex]

altså:

[tex]{d\over dx}[{log_{10}(x)}]\;=\;[/tex][tex]{d\over dx}[{ln(x)\over ln(10)}][/tex][tex]\;=\;{1\over xln(10)}[/tex]

q.e.d.