FIND Y" if Y=ln(sec(x)+tan(x))

Answer 1

first simplify the inside
sec(x)+tan(x)
= (1 + sinx)/cosx

then y=ln(sec(x)+tan(x))
= ln((1 + sinx)/cosx)
= lin(1 + sinx) - ln(cosx)

y' = cosx/(1+sinx) - (-sinx)/cosx
= cosx/(1+sinx) + tanx

now differentiate this once more.