Find `d/dx((1-tan^2x)/(1+tan^2x))`

Find d/dx (tan^-1(tanx)) when - pi/2 < x < pi/2

For the following differentiation results, write down the corresponding results in integrations: d/(dx)(tan^-1x)=1/(1+x^2)

Find d/(dx)(1/(sqrt(1-x^2))

d/dx(e^(2sin^-1x)) =

Find d/(dx)(e^(sqrt(1+x^2)))

d/dx{tan^-1sqrtx} =

d/dx{tan^-1((x+a)/(1-ax))} = __________

Differentiate cos^(-1)((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)x .

Differentiate tan^(-1)((2x)/(1 - x^2)) w.r.t. sin^(-1)((2x)/(1 + x^2))

Differentiate the following w.r.t. x: tan^-1(2x/(1-x^2)), 0 < x < 1