Find the derivatives of the functionlog(tan x)

1.	Find the derivatives of the functionlog(tan x)
Answer» Assume tan x to be y then the question becomes to find the derivative of log y. Hence, d/dx log (tan x) = 1/tan x . d/dx (tan x) ( using d/dx log x = 1/x) = 1/tan x . sec2x. = (cos x)/ (sin x). 1/ cos2x = 1/ sin x cos x This is the answer which if required can further be simplified as 2/ 2sin x cos x which becomes 2/ sin 2x = 2 cosec 2x.

Answer»

Assume tan x to be y then the question becomes to find the derivative of log y.

Hence, d/dx log (tan x) = 1/tan x . d/dx (tan x) ( using d/dx log x = 1/x)

= 1/tan x . sec2x.

= (cos x)/ (sin x). 1/ cos2x

= 1/ sin x cos x

This is the answer which if required can further be simplified as 2/ 2sin x cos x

which becomes 2/ sin 2x = 2 cosec 2x.

Discussion