If y = cos^-1(2x) + 2cos^-1√(1 - 4x^2), 0 < x < 1/2, find dy/dx.

Question

If y = cos^-1(2x) + 2cos^-1\(\sqrt{1-4 \mathrm x^2},\) 0 < x < \(\cfrac12,\) find \(\cfrac{dy}{d\mathrm x}\).

Answer 1

 y = cos^-1(2x) + 2cos^-1\(\sqrt{1-4 \mathrm x^2}\)

Put 2x = cos θ

Differentiating w.r.t x we get