Question #ec712

1 Answer
Apr 7, 2017

d/dxtan^2x=2tanx*sec^2xddxtan2x=2tanxsec2x

d/dxsec^2x=2sec^2xtanxddxsec2x=2sec2xtanx

Explanation:

d/dxtan^2xddxtan2x

Apply chain rule,

r(u)^(r-1)*d/(du)r(u)r1ddu

=2tanx*d/dx(tanx)2tanxddx(tanx)

d/dxtanx=sec^2xddxtanx=sec2x (common derivative)

Therefore the final answer is,

d/dxtan^2x=2tanx*sec^2xddxtan2x=2tanxsec2x


d/dxsec^2xddxsec2x

Apply chain rule

r(u)^(r-1)*d/(du)r(u)r1ddu

2secx*d/(dx)secx2secxddxsecx

d/(dx)secx=secx*tanxddxsecx=secxtanx (common derivative)

Therefore the final answer is,

d/dxsec^2x= 2secx*secx*tanx*ddxsec2x=2secxsecxtanx

Which simplifies to,

d/dxsec^2x=2sec^2xtanxddxsec2x=2sec2xtanx