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Print 21. Let flu) = 1/u and g(x) = u=1+9x2. Find (fog)(1). (fog)'(1) = (Type an exact answer.) 22. Use the Chain Rule to differentiate

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Print 21. Let flu) = 1/u and g(x) = u=1+9x2. Find (fog)"(1). (fog)'(1) = (Type an exact answer.) 22. Use the Chain Rule to differentiate the following function. f(x ) = 4x2+ 1-3x3 f' (x) = 23. Differentiate. y= 1x3 + 12x+3 .x3 y' = 24. Differentiate. f(x) = =10x+ vx f (x) = 25. The position of a particle moving along a coordinate line is s = v7 + 6t, with s in meters and t in seconds. Find the rate of change of the particle's position at t = 3 sec. The rate of change of the particle's position at t = 3 sec is m/ sec. Type an integer or a simplified fraction.) 20. If $1000 is invested at interest rate i, compounded annually, in 5 yr it will grow to an amount A given by A = $1000(1 + 1). dA a) Find the rate of change. - di b) Interpret the meaning of - dA di . dA a) di Simplify your answer. Use integers or fractions for any numbers in the expression. Do not include the $ symbol in your answer.) b) Choose the correct answer below. O A. dA is the rate at which A changes due to changes in the number of years passed. O B. dA is the rate at which A changes due to changes in the initial investment. O C. - is the rate at which A changes due to how often interest is compounded. dA OD. is the rate at which A changes due to changes in the interest rate i. 27. The dosage for a certain type of chemotherapy drug depends on several parameters of the particular drug as well as the age, weight, and sex of the patient. For female patients, the formulas giving the dosage for such drugs are D = 0.85A(c+ 25) and c = (140 -Y),,". where A and x depend on which drug is used, D is the dosage in milligrams (mg), c is called the creatine clearance, y is the patient's age in years, and w is the patient's weight in kilograms. Complete parts (a) through e) below a) Suppose that a patient is a 44-year-old woman and the drug has parameters A = 3 and x = 0.5. Use this information to write formulas for D and c that give D as a function of c, and c as a function of w. D(c) = c(w) = (Simplify your answers. Round to three decimal places as needed.) b) Use your formulas from part (a) to compute - dD do (Simplify your answer. Round to three decimal places as needed.) c) Use your formulas from part (a) to compute dy dc (Simplify your answer. Round to three decimal places as needed.) d) Compute - dD dw dD dw (Simplify your answer. Round to three decimal places as needed.)

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