If y=sin−1(x√1−x+√x√1−x2) then dydx=
−2x√1−x2+12√x−x2
−1√1−x2−12√x−x2
1√1−x2+12√x−x2
None of these
Putting x=sin A and √x=sin B ⇒y=sin−1(sin A√1−sin2B+sin B√1−sin2A) =sin−1[sin(A+B)]=A+B=sin−1x+sin−1√x ⇒dydx=1√1−x2+12√x−x2
Find dydx, if y=sin−1x+sin−1√1−x2,−1≤x,≤1.