ddxsin(x2)=\dfrac{d}{dx}\sqrt{\sin(x^2)} =dxdsin(x2)=A2xcos(x2)\dfrac{2x}{\cos(x^2)}cos(x2)2xBsin(x2)2x\dfrac{\sin(x^2)}{2x}2xsin(x2)Cxcos(x2)sin(x2)\dfrac{x \cos(x^2)}{\sqrt{\sin(x^2)}}sin(x2)xcos(x2)check_circleDcos(x2)2sin(x2)\dfrac{\cos(x^2)}{2\sqrt{\sin(x^2)}}2sin(x2)cos(x2)ExplanationOuter: 12sin(x2)\dfrac{1}{2\sqrt{\sin(x^2)}}2sin(x2)1. Middle: cos(x2)\cos(x^2)cos(x2). Inner: 2x2x2x. Product: 2xcos(x2)2sin(x2)=xcos(x2)sin(x2)\dfrac{2x\cos(x^2)}{2\sqrt{\sin(x^2)}} = \dfrac{x\cos(x^2)}{\sqrt{\sin(x^2)}}2sin(x2)2xcos(x2)=sin(x2)xcos(x2).