Differentiate each of the following w.r.t. x

We have given tan^-1(sec x + tan x)

Let us Assume (sec x +tan x) =t

SO, y = tan^-1 t

Now, differentiate w.r.t t

Since,

And, t= (sec x+tan x)

Differentiate t w.r.t x

Therefore,

When, substitute the value of t we get

Hence, dy/dx=1/2