Differentiate the following functions with respect to x:
sin–1 (1 – 2x2), 0 < x < 1
Now
Using 1 – 2sin2θ = cos2θ
y = sin–1(cos2θ)
Considering the limits,
0 < x < 1
0 < sin θ < 1
0 < 2θ < π
0 > –2θ > –π
Now,
Differentiating w.r.t x, we get