How do you differentiate #ln(cos^2(x))#?

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Answer 1 · 2018-05-29T08:17:27

#-2tanx#

#d/dx[ln(cos^2(x))]#

Differentiate,

#1/(cos^2(x))*d/dx[cos^2(x)]#

Differentiate second term,

#1/(cos^2(x))*-2sinxcosx#

Multiply,

#-(2sinxcancel(cosx))/(cos^cancel(2)(x))#

Simplify,

#-(2sinx)/(cosx)#

Refine,

#-2tanx#

Answer 2 · 2018-05-29T10:03:20

As above

Alternatively, you could say:
#ln(cos^2(x)) = 2ln(cosx)#

Then:
#d/dx(ln(cos^2(x)))#
# = 2*d/dx(ln(cosx))#
# = 2* (-sinx)/cosx#
#= -2tanx#