Câu hỏi 32

\(\begin{array}{l}y' = \left[ {\sin \left( {{{\cos }^2}x} \right)} \right]'.\cos \left( {{{\sin }^2}x} \right) + \sin \left( {{{\cos }^2}x} \right).\left[ {\cos \left( {{{\sin }^2}x} \right)} \right]'\\y' = \cos \left( {{{\cos }^2}x} \right).\left( {{{\cos }^2}x} \right)'.\cos \left( {{{\sin }^2}x} \right) - \sin \left( {{{\cos }^2}x} \right).\sin \left( {{{\sin }^2}x} \right).\left( {{{\sin }^2}x} \right)'\\y' = \cos \left( {{{\cos }^2}x} \right).2\cos x\left( {\cos x} \right)'.\cos \left( {{{\sin }^2}x} \right) - \sin \left( {{{\cos }^2}x} \right).\sin \left( {{{\sin }^2}x} \right).2\sin x\left( {\sin x} \right)'\\y' =  - \cos \left( {{{\cos }^2}x} \right).2\cos x.\sin x.\cos \left( {{{\sin }^2}x} \right) - \sin \left( {{{\cos }^2}x} \right).\sin \left( {{{\sin }^2}x} \right).2\sin x.\cos x\\y' =  - 2\sin x\cos x\left[ {\cos \left( {{{\cos }^2}x} \right).\cos \left( {{{\sin }^2}x} \right) + \sin \left( {{{\cos }^2}x} \right).\sin \left( {{{\sin }^2}x} \right)} \right]\\y' =  - \sin 2x.\cos \left( {{{\cos }^2}x - {{\sin }^2}x} \right)\\y' =  - \sin 2x.\cos \left( {\cos 2x} \right)\\ \Rightarrow a =  - 1 \in \left( { - 3;2} \right)\end{array}\)

Chọn C.