2.1 y=7x*lnx
y'=(7x)'*lnx+7x*(lnx)=7*lnx+7x/x=7*lnx+7=7*(lnx+1).
2.2 y=x²/(x+2)
y'=((x²)'*(x+2)-x²*(x+2)')/(x+2)²=(2x*(x+2)-x²*1)/(x+2)²=
=(2x²+4x-x²)/(x+2)²=(x²+4x)/(x+2)²=x*(x+4)/(x+2)².
2.3y=6*⁷√x⁵+5/x³+1 x₀=1.
y'=(6*x⁵/⁷+5*x⁻³+1)'=6*(5/7)*x⁻²/⁷+5*(-3)*x⁻⁴=(30/7)*x²/⁷-15*x⁻⁴
==30/7-15=4²/₇-15=-11⁵/₇.