for each of the following functions. 2. Find the derivative (a) f(x) = ( (b) g(x) = (x sin x]* 3. A tank contains pure water. Brine (salt solution) is added to the tank. At any time x the concentration of salt in the tank is given by 30x C(x) = 200 + x where x is measured in minutes (min) and C is measured in grams per liter (g/L). (a) Find the average rate of change of concentration between 20 minutes and 30 minutes. Give your answer correct to three decimal places. State your answer in proper units. (b) Find the instantaneous rate of change of concentration at time x = 30 minutes. Give your answer correct to three decimal places. State your answer in proper units. 4. A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei. The brightness f(t) of Delta Cephel at timet is given by f(t) = 4.0 + 3.5 sin (4) where f is measured in lumens and t is measured in days. (a) Find the average rate of change in brightness between t = 2 and t = 4 days. Give your answer correct to two decimal places. Give proper units. (b) Find the instantaneous rate of change in brightness at t = 3 days. Give your answer correct to two decimal places. Give proper units. 5. Find for 2xy + At sin(xy) = 27 and use it to find the slope of tangent at the point (1) 6. Find for x3 - 4xy + 2y2 = 13 and use it to find the equation of tangent at the point (2,1).