Question Detail

To find the derivative of y = log(sec x + tan x) (assuming natural logarithm, ln), we use the chain rule.d/dx (ln u) = (1/u) * du/dxHere, u = sec x + tan x.First, find du/dx:du/dx = d/dx (sec x) + d/dx (tan x)= sec x tan x + sec² xNow, apply the chain rule:dy/dx = (1 / (sec x + tan x)) * (sec x tan x + sec² x)Factor out sec x from the numerator:dy/dx = (1 / (sec x + tan x)) * (sec x (tan x + sec x))Cancel out (sec x + tan x):dy/dx = sec xThis matches option C.