How do you find the derivative of y=ln(cos(x))y=ln(cos(x)) ?

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21-09-2014
Mathematics

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How do you find the derivative of y=ln(cos(x))y=ln(cos(x)) ?

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Аноним Аноним · Answer 1 · 2014-09-21T04:34:30-04:00

Аноним Аноним

21-09-2014

[tex]y=ln(cosx)\\\\We\ know:\\(lnx)'=\frac{1}{x}\ and\ (cosx)'=-sinx\ and\ \{f[g(x)]\}'=f'[g(x)]\cdot g'(x)\\\\therefore:\\\\y'=\frac{1}{cosx}\cdot(-sinx)=-\frac{sinx}{cosx}=-tanx[/tex]

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