I was just wondering where the y'/(dy/dx) in implicit differentiation comes from

${x}^{2}+{y}^{2}=25$

$(d/dx){x}^{2}+(d/dy){y}^{2}\ast \ast (dy/dx)\ast \ast =25(d/dx)$

$2x+2y(dy/dx)=0$

$(dy/dx)=-x/y$

Where does the bold part come from?

${x}^{2}+{y}^{2}=25$

$(d/dx){x}^{2}+(d/dy){y}^{2}\ast \ast (dy/dx)\ast \ast =25(d/dx)$

$2x+2y(dy/dx)=0$

$(dy/dx)=-x/y$

Where does the bold part come from?