`(d)/(dx)[tanx]=?`

prove that (d)/(dx)[(1-tanx)/(1+tanx)]^(1/2)=(-1)/((sqrt(cos2x))cosx)

(d)/(dx)[tan^(-1)[(secx-tanx)]=

(d)/(dx)[tan^(-1)((2+3tanx)/(3-2tanx))]=

(d)/(dx)[tan^(-1)(cotx)+cot^(-1)(tanx)]=

d/(dx){x^(tanx)} =

(d)/(dx)((cotx-tanx)/(cotx+tanx))=

(d)/(dx)((secx+tanx)/(secx-tanx))=

For the following differentiation results, write down the corresponding results in integrations: d/(dx)(e^tanx)=e^tanx sec^2 x

d/dx(log tanx) =