I have the following task: "Poiscuille's Law: $V=\frac{P}{4Lv} (R^2 - r^2)$. Assume that $r$ is a constant as well as $P,L,v$. Find the rate of change $\frac{dV}{dt}$ in terms of $R$ and $\frac{dR}{dt}$ when $L=1$mm, $p=100$, $v=0.05$."
I cannot understand how can how can diff that, what is the $t$ here? I can write $V = 500 (R^2 - r^2)$. But what after? And what is "find the rate of change in terms of...? Something like: $\frac{dV}{dt} = \frac{dV}{dR}\frac{dR}{dt}$? I am right?
You have a function $$V(R)=\frac{p}{4Lv}(R^2-r^2)$$ But $R$ is a function of the time, so you have that $$V(t)=V(R(t))=\frac{p}{4Lv}(R^2(t)-r^2)$$ So you are right, you should just use the chain rule.