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now well consider a few examples where we will do rate of change with respect to dimensions of geometric figures now this one is for area of circle so here we have two related questions and lets try to understand them the first one is find the rate of change of the area of a circle with respect to its radius when R equals to 6 centimeter and the second part is how is the rate of change of the area of a circle related with its radius when radius is R so lets find a relation between radius and area of circle and then do its derivative derivative after all is rate of change so the relation between area and radius is that area is equals to PI R squared so thats the relation between area and radius of a circle now here any as a function of radius so I can write this as P of R so it becomes in function notation since area is a function of radius we can find derivative of this with respect to R so we have derivative of a of R with respect to R equals 2 derivative d dr of pi r square now s