arccos(2x-1)=2arccosx

Question

arccos(2x-1)=2arccosx

Answer 1

f'(x) = -2/sqrt(1 - x^2) - [-(2x-1)']/sqrt(1-2x+1)(1+2x-1)

f'(x) = -2/sqrt(1 - x^2) + 2/sqrt 4x(1-x)

f'(x) = -2/sqrt(1 - x^2) + 2/2sqrt x(1-x)

f'(x) = -2/sqrt(1+x)(1-x) + 1/sqrt x(1-x)

f'(x) = [-2sqrtx + sqrt(1+x)]/sqrt x(1 - x^2)