Ответ:

[tex]y=(x+3)*(x^6-1)\\\\y'=(x+3)'*(x^6-1)+(x^6-1)'*(x+3)=1*(x^6-1)+6x^5*(x+3)=x^6-1+6x^6+18x^5=7x^6+18x^5-1[/tex]

[tex]y=x^2cos(x)\\\\y'=(x^2)'*cos(x)+(cos(x))'*x^2=2x*cos(x)-x^2*sin(x)=2xcos(x)-x^2sin(x)[/tex]

Ответ:

Производная произведения:  [tex]\bf (uv)'=u'v+uv'[/tex]  .

[tex]\bf 1)\ \ y=(x+3)(x^6-1)\\\\y'=1\cdot (x^6-1)+(x+3)\cdot 6x^5=x^6-1+6x^6+18x^5=7x^6+18x^5-1\\\\\\2)\ \ y=x^2\cdot cosx\\\\y'=2x\cdot cosx+x^2\cdot (-sinx)=2x\cdot cosx-x^2\cdot sinx[/tex]