We know that,
color(red)((1)d/(dx)(secx)=secxtanx(1)ddx(secx)=secxtanx
color(green)((2)d/(dx)(tanx)=sec^2x(2)ddx(tanx)=sec2x
Here,
y=sec^2x+tan^2xy=sec2x+tan2x
Diff.w.r.t. xx ,"using "color(blue)"Chain Rule :"using Chain Rule :
(dy)/(dx)=2secxcolor(red)(d/(dx)(secx))+2tanx color(green)(d/(dx)(tanx)dydx=2secxddx(secx)+2tanxddx(tanx)
:.(dy)/(dx)=2secx*color(red)(secxtanx)+2tanx*color(green)(sec^2x
:.(dy)/(dx)=2sec^2xtanx+2sec^2xtanx
:.(dy)/(dx)=4sec^2xtanx