Find The Derivative Y = In (Tan X + Sec X)

Find the derivative y = In (tan x + sec x)

 

y = ln (tan x + sec x)

dy/dx (ln x) = 1/x dx

dy/dx (tan x) = sec^2 x dx

dy/dx (sec x) = sec x tan x dx

d/dx (u/v) = (vdu - udv) / (v^2)

y = 1/(tan x + sec x)

y = (tanx + sec x) - (sec^2 x + secx tanx) / (tanx + sec x)^2

y = (tanx + secx - sec^2x - secxtanx) / (tan^2x + 2tanxsecx + sec^2)

Inform me if I made a mistake.