Related rates
= Related rates
Related rates use the <chain rule> to connect time <derivatives> of quantities constrained by an equation. If $F(x(t),y(t))=0$, differentiating gives $F_x\dot x+F_y\dot y=0$. For a <rectangle> with one fixed side $a$ and variable side $b(t)$, its diagonal $d(t)=\sqrt{a^2+b(t)^2}$ obeys $\dot d=(b/d)\dot b$. The equation must be differentiated before inserting an instantaneous value of $b$, since that value does not make the changing side constant in time.