1) 9x^3 + 7х^2 - 11х + 68
y'=27x^2+14x-11
2) 5х^-2
y'=-10x^-3
3) 1/х
y'=-1/x^2
4) sinx + cosx - x
y'=cosx-sinx-1
5) e^x · ln x
y'=e^x *lnx + e^x * 1/x
6) x^2 · cosx
y'=2x*cosx + x^2*(-sinx)
7) 5sinx · cosx
y'=5cosx*cosx+5sinx*(-sinx) =5cos^2x -5sin^2x=5cos2x
8) (x+x^2) / (2x+5)
y'=[ (1+2x)(2x+5)- (x+x^2)*2 ] / (2x+5)^2 = [ 2x+5+4x^2+10x-2x-2x^2]/(2x+5)^2=
=[2x^2+10x+5] /(2x+5)^2
9) cosx / sinx
=ctgx
y'=-1/sin^2x
10) (x^3 +7) / (x+4)
y'=[ 3x^2*(x+4) - (x^3+7)*1 ] /(x+4)^2 = [3x^3+12x^2-x^3-7] / (x+4)^2 =
=[2x^3+12x^2-7] /(x+4)^2