Question

Найти прозводную.
а). у=(5х+sin^2x)*(x^2-cos2x)
б). y=(1-2sin^2x)*(1-cos3x)

Answer 1

a)y`=(5+2sinxcosx)(x²-cos2x)+(5x+sin²x)(2x+2sin2x)=
=(5+sin2x)(x²-cos2x)+(5x+sin²x)(2x+2sin2x)=
=5x²-5cos2x+x²sin2x-sin2xcos2x+10x²+10xsin2x+2xsin²x+2sin²xsin2x=
=15x²-5cos2x+x²sin2x-1/2sin4x+10xsin2x+2xsin²x+2sin²xsin2x
b)y`=-4sinxcosx(1-cos3x)+3sin3x(1-2sin²x)