Question

Find the differential dy of the given function.
y=sec^2x/(x^2+1)

My answer was [tanx(x^2+1)-2sec^2x]dx/(x^2+1)^2

My friend (who's a lot smarter than me) got something wayyy different, so I'm not sure if I'm doing this wrong...?

Answer 1

[(x^2+1)d(sec^2x)-sec^2xd(x^2+1)]/(x^2+1)^2

[(x^2+1)2secxdsecx-sec^2x(2xdx)]/(x^2+1)^2

[2(x^2+1)sec^2xtanxdx-2xsec^2xdx]/(x+1)^2

2 sec^2 x dx [(x^2+1)tan x - x ]/ (x+1)^2

Answer 2

Wait, I'm not understanding how you get the tanx -x part...

Answer 3

Hold on...I think I just managed to kind of figure it out!