Did I do this problem right?

Question

Find the first and second derative-simplify your answer.

y=xtanx

y'= (x)(sec^2 x)+(tanx)(1)
y'= xsec^2 x + tanx

y"= (x)(2secx)(secxtanx)+sec^2 x + sec^2 x
y"=2xsec^2 x tanx + 2 sec^2 x

Answer 1

= 2 sec^2x(x tan x + 1)