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...
... is the product rule - straight continuous lines differentiating downwards (integrating up) with respect to t.
Don't integrate - balloontegrate!
Balloon Calculus: standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!