The rates to relate are of R, p and q, and since R=pq we can see that differentiating them all with respect to t will involve the product rule. I would think...

... where

... is the product rule - straight continuous lines differentiating downwards (integrating up) with respect to t.

Spoiler:

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Don't integrate - balloontegrate!

Balloon Calculus: standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!