a. y′=4sin3x(sinx)′=4sin3x.cosx=2sin2x.sin2x
b. y′=4cos32x(cos2x)′=−4cos32x.sin2x.(2x)′=−8cos3x.sin2x
c. y′=(x2−1)′.(x3+2)+(x3+2)′.(x2−1)=2x(x3+2)+3x2(x2−1)=5x4−3x2+4x
d. y′=(cos3x)′.sin22x+(sin22x)′.cos3x=−sin3x(3x)′.sin22x+2sin2x(2x)′.cos3x=−3sin3x.sin22x+4sin2x.cos3x