y = sinh^-1(tanx) Find the derivative of the function

Given
y=sinh^-1 (tanx)
to find
y' = (sinh^-1 (tanx))'
let u=tanx
 
so ,
y' = d/(du) (sinh^-1 (u)) d/dx tanx
=1/sqrt(u^2+1) sec^2x
=(sec^2 x)/sqrt(tan^2+1)