4) y'=5*(x^4+2x^3)^4*(4x^3+6x^3)=10x^14*(x+2)^4*(2x+3)
5) y'=3ln^2(ctg5x)*(1/ctg5x)*(-1/sin^25x)*5=
=-15ln^2ctg5x*sin5x/(cos5x*sin^25x)=
=-30ln^2ctg5x/sin10x
6) y'=(-3√x*sinx-3/(2√xcosx))/x=-(3/2)*(2xsinx-cosx)/x√x
Объяснение:
4) y'=(x^4+2x^3)^5=5(x^4+2x^3)^4*(x^4+2x^3)'=5(x^4+2x^3)^4*(4x^3+6x^2);
5) y'=(Ln³ctg5x)' =( 1/(ctg5x))*(ctg5x)'=( 1/(ctg5x))*(-1/sin²5x)*5=-5/(ctg5x*sin²5x=-5/(cos5x*sin5x)=-5/(sin(10x))/2=-10*sin(10x
6) y'=(3cosx/√x)'=3*(cosx*(√x)'+cosx'*(√x))=3*(cosx*1/2√x-sinx√x)=3(cosx-2xsinx)/2√x=1,5((cosx-2xsinx)√x
