Math Is Fun Forum

Hello,

A population grows exponentially.

is the flow of births at time t, where p(t, x) is the proportion of those born t-x years ago and still alive at age x and m(t, x) is the proportion of those reproducing at age x at time t.

It follows:

(1)

According to the author "using the appropriate chain rule" it follows from (1) that:

What is the "appropriate chain rule" the author is talking about? Unfortunately, I only know one chain rule. Could someone show me an intermediate step, please?

Thanks in advance and best regards,
Sebastian