y= tan(2tan^-1x/2), show that dy/dx= 4(1+y^2)/4+x^2

Answer 1

y = tan(2arctan(x/2))
arctan(y) = 2arctan(x/2)
1/(1+y^2) y' = 4/(4+x^2)
y' = 4(1+y^2)/(4+x^2)

Answer 2

Answer