I am reading a paper, the author takes the derivative of the following equation with respect to $t$: $$ q(t) = \int_t^\infty e^{-r(s-t)}c(s)e^{-\delta(s-t)}ds $$

  • $q$ price of capital goods
  • $r$ discount rate
  • $c$ cost of goods
  • $\delta$ rate of replacement
  • $t$ time of acquisition of goods
  • $s$ time of supply of goods

I have the answer, but I was hoping someone would explain the intermediate points. Here, is the process similar to differentiating the functions with summation operators in discrete cases?

  • $\begingroup$ It's just the Leibniz rule: en.wikipedia.org/wiki/Leibniz_integral_rule $\endgroup$ – Herr K. Feb 26 '16 at 19:29
  • $\begingroup$ Can you please include in your question an expression that exemplifies the discrete case you have in mind? $\endgroup$ – Alecos Papadopoulos Feb 26 '16 at 19:38
  • $\begingroup$ @Alecos, I mean the Riemann sum. $\endgroup$ – london Mar 1 '16 at 12:12
  • $\begingroup$ Can anyone walk me through the solution? Thanks! $\endgroup$ – london Mar 1 '16 at 12:13

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