Calculate p'(t) 4.2t-0.9 - 0.6t-0.5 p(t) = 0.4 + +0.1 a. p'(t) = (3.36t-18 + 0.3t-1.5)(0.4 + +0.1) + (0.12-0.9) (4.2t-0.8 - 0.6t-0.5) (0.4 + +0.1)2 b. p'(t) _ (3.36t + 0.3t-15)(0.4 + +0.1) - (0.4 + 0.1t-0.9) (4.2t-0.8 - 0.6t-0.5) (0.4 + +0.1)2 c. p'(t) =. (-3.36t -18 + 0.3t-15)(0.4 + +0.1) - (0.1t-0.9) (4.2t-0.8 - 0.6t-0.5) (0.1t-0.9)2 d. p'(t) = (-3.36t -18 + 0.3t-15)(0.4 + +0.1) - (0.1t-09) (4.2t-0.8 - 0.6t-0.5) (0.4 + +0.1)2 e. p'(t) = (0.1t-0.9)(4.2t-0.8 - 0.6t-0.5) - (-3.36t-18 + 0.3t-15) (0.4 + + 0.1) (0.4 + +0.1)2 f. p'(t) = - -3.36t-18 + 0.3t-15 0.1t-0.9\fCalculate v"(t) v(t) = - 14 t a. v" (t) = b. v"(t) = C. v"(t) = d. v"(t) = 28 e. v" (t) = 28 f. v" (t) = -73Worldwide annual sales of cellphones in 2012-2013 were approximately q = 6p + 3060 million phones at a selling price of Sp per phone. 1With a manufacturing cost of $50 per phone, what selling price would have reSulted in the largest annual prot? The total amount spent on research and development by the federal government of the United States during the years 2000 - 2012 can be approximated by: S(t) = 29In(256t + 2860) in billions of dollars Where t is the years since 2000. What was the total spent in 2009 and how fast was it changing? (Round your results to 3 decimal places)Daily crude oil imports to the U5. from Mexico for 2001 4013 is approximated by: {{r) = E'.'3t2 + 300: 3000 in thousands of barrels Where t is the time in years since the start of 2001. Find the derivative function Ht) . At what rate were oil imports changing at the start of 2006