The speed S of blood that is r centimeters from the center of an artery is given below, where C is a constant, R is the radius of the artery, and S is measured in centimeters per second. Suppose a drug is administered and the artery begins to dilate at a rate of dR/dt. At a constant distance r, find the rate at which S changes with respect to t for C = 1.42 X 10^5, R = 1.0 X 10^-2, and dR/dt = 2.0 X 10^-5. (Round your answer to 4 decimal places.)

Question

S = C(R^2 − r^2)

dS/dt = cm/s

Answer 1

you just want dS/dt, which is just
dS/dt = 2CR dR/dt - 2Cr dr/dt

Now just plug in your values. Note that if r is constant, dr/dt = 0