Partial Derivatives of Functions of Two Variables

    Problem 1. The concentration C of a drug in the blood (in mg per liter) following its injection is a function of the dose x (in mg) and the time t (in hours) since the injection: C = xte−t (a) Find C| (x,t)=(5,1). What does this tell you about the concentration of drug in the blood stream? (b) Find a formula for the section where x = 5 and use it to find ∂C ∂t (x,t)=(5,1) What are the units? What does this value tell you about the concentration of drug in the blood stream? (c) Find a formula for the section where t = 1 and use it to find ∂C ∂x (x,t)=(5,1) What are the units? What does this value tell you about the concentration of drug in the blood stream?