a) y=(3+6x)/(√(3-4x+5x²) 6√(3-4x+5x²)-(3+6x)(-4+10x) ----------------- 2√(3-4x+5x²) 6(3-4x+5x²)-(3+6x)(-2+5x)y' = -------------------------------------------- = -----------------------------------------= (3-4x+5x²) (3-4x+5x²) √(3-4x+5x²) 30x²-24x+18 +6+12x-15x-30x² -27x +24= ----------------------------------------- = --------------------------------------- (3-4x+5x²) √(3-4x+5x²) (3-4x+5x²) √(3-4x+5x²) б) у=sinx-xcosx y'= cosx-(cosx-x·sinx)в) у=(x^m)㏑x y'=mx^(m-1)㏑x +(x^m)/x= mx^(m-1)㏑x +x^(m-1)=x^(m-1)(m㏑x +1)г) y=x^(-tgx)ln y = -tgx ·lnxy'/y = -[(1/cos²x)lnx+(tgx)/x] ⇒ y' = -y[(1/cos²x)lnx+(tgx)/x] y' = -x^(-tgx)·[(1/cos²x)lnx+(tgx)/x]д) y/x= arctg(x/y) (y'x -y)/x²={1/(1+(x/y)²)}·{(y-y'x)/y²} y'·(1/x+x/(x²+y²))=y/(x²+y²)-y/x²y'=y(1/(x²+y²)-1/x²)/(1/x+x/(x²+y²))y'=-y³/(x(x²+y²-1))