What is the derivative of $f (x) = {log}_{2} (cos (x))$ $f(x)=log_2(cos(x))$ ?

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Answer 1 · 2018-03-18T15:36:58

$- \frac{tan (x)}{ln (2)}$ $-tan(x)/ln(2)$

$f (x) = {log}_{2} (cos (x)) = \frac{ln (cos (x))}{ln (2)}$ $f(x)=log_2(cos(x))=ln(cos(x))/ln(2)$

$\frac{1}{ln (2)}$ $1/ln(2)$ is just a constant and can be ignored.

$(ln(u))'=(u')/u$

$u=cos(x), u'=-sin(x)$

$f'(x)=1/ln(2)*(-sin(x))/cos(x)=-tan(x)/ln(2)$

What is the derivative of f(x)=log_2(cos(x))f(x)=log2(cos(x))f(x)=log_2(cos(x)) ?