What is the derivative of #ln((tan^2)x)#?

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Answer 1 · 2016-06-02T15:20:02

#d/dx(ln(tan^2 x))=2*(tan x+cot x)##

The given is #ln (tan^2 x)#

#d/dx(ln (tan^2 x))=1/(tan^2 x)*d/dx(tan^2 x)#

#d/dx(ln (tan^2 x))=1/(tan^2 x)*2(tan x)^(2-1)*d/dx(tan x)#

#d/dx(ln (tan^2 x))=1/(tan^2 x)*2*tan x*sec^2 x#

#d/dx(ln (tan^2 x))=1/(tan x)*2*sec^2 x#

#d/dx(ln (tan^2 x))=(2*(tan^2 x+1))/(tan x)#

#d/dx(ln (tan^2 x))=2*(tan x+cot x)#

God bless......I hope the explanation is useful.