Question

find the derivative of log (tanh x)?​

Answer 1

Answer:

1/(tan x) sec2x

Step-by-step explanation:

y=log(tan x)

duff. w. r. t. x

dy/dx=d/dx log (tan x)

=1/(tan x) d/dx(tan x)

=1/(tan x) sec2x

or

=sec2x/tan x

Answer 2

Answer:

2cosech(2x)

Step-by-step explanation:

let y=log (tanh x)

diff. both sides w.r.t x

dy/dx = d log(tanhx)/dx

dy/dx =d log(tanhx)/dtanhx * dtanhx/dx

dy/dx = 1/tanhx * sech^2 x

dy/dx = coshx/sinhx * 1/cosh^2

dy/dx = 2/2sinhx.coshx

dy/dx = 2/sinh(2x)

dy/dx = 2cosech(2x)