f(x)=x*lnx такое?
f'(x)=x' lnx+xlnx'=lnx+x*1/x=lnx+1
или
f(x)=x*sinx
f'(x)=sinx+x*cosx
f(x) ' = (x* sin(x) ) ' = sin(x) +x*cos(x)
