Differentiate the following functions with respect to x:
Let ax = tanθ
Considering the limits,
–∞ < x < 0
a–∞ < ax < a0
0 < tanθ < 1
Now,
y = tan–1(tan2θ)
y = 2θ
y = 2tan–1(ax)
Differentiating w.r.t x, we get