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

1 Answer

Mar 18, 2018

#-tan(x)/ln(2)#

Explanation:

#f(x)=log_2(cos(x))=ln(cos(x))/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)#

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