Question

Tan-1(1+x/1-x)^1/2find dy/dx

Answer 1

arctan sqrt[(1+x)/(1-x)]
dy/dx = {sqrt[(1+x)/(1-x)]}'/{1+[sqrt[(1+x)/(1-x)]]^2}
dy/dx = [(1+x)/(1-x)]'/2{sqrt[(1+x)/(1-x)]}*{1+(1+x)/(1-x)}
[(1+x)/(1-x)]' = (1-x-1-x)/(1-x)^2=-2x/(1-x)^2
dy/dx = -2x(1-x)/4*(1-x)^2*{sqrt[(1+x)/(1-x)]}
dy/dx = -x/2*(1-x)*{sqrt[(1+x)/(1-x)]}