How do you differentiate y=sec^2x+tan^2xy=sec2x+tan2x?

1 Answer
Jul 27, 2018

(dy)/(dx)=4sec^2xtanxdydx=4sec2xtanx

Explanation:

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