find dy/dx

Question

y=ln (secx + tanx)

Let u= secx + tan x

dy/dx= 1/u * du/dx

now, put the derivative of d secx/dx + dtanx/dx in. You may have some challenging algebra to simplify it.

Use the chain rule. Let y(u) = ln u
u(x) = sec x + tan x
dy/dx = dy/du*du/dx

dy/du = 1/u = 1/(sec x + tan x)
dy/dx = sec x tan x + sec^2 x
= sec x (sec x + tan x)
dy/dx = sec x

Answer 1

(sec x + tan x)

So, the derivative dy/dx of y = ln(sec x + tan x) is:

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