Let # y= tanx^secx + secx^cotx#
Let #u=tanx^secx# and #v=secx^cotx#
#lnu = secxlntanx#
#1/u# #(u')= secxtanxlntanx + sec^2xcscx#
#u' = u(secxtanxlntanx + sec^2xcscx) = (secxtanxlntanx+sec^2xcscx)tanx^secx#
#lnv = cotlnsecx#
#1/v# #(v') = -csc^2xlnsecx + 1#
#v'= v(1-csc^2xlnsecx) =(1-csc^2xlnsecx)secx^cotx#
#dy/dx = (secxtanxlntanx+sec^2xcscx)tanx^secx + (1-csc^2xlnsecx)secx^cotx#