Please help in explaining the following. Hand written answers are appreciated

(1) Differentiate each of the following functions, using any appropriate method. (a) f(x) = 270 (b) h() = - 4- 23 (c) f(x) = 3xe (d) f(x) = cos(x) (e) f(x) = tan(sin(z)) (f) g(x) = In(2x2 + 4x + 3) (2) Use implicit differentiation to find y'. a2 - 4y2 = 12 (3) Use logarithmic differentiation to find y'. y = (24+ 2)2(22 - 3)4 (4) The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of 2cm/s. When the length 20cm and the width is 10cm, how fast is the area of the rectangle increasing? (5) Explain why the function f(x) = 23 - 3x2 + 1 must have an absolute maximum and absolute minimum value on [-2, 4). Find the absolute maximum and absolute minimum values of f on [-2, 4] (6) Verify that the function f(x) = 2x2 -3x + 1 satisfies the hypotheses of the Mean Value Theorem on the interval [0, 2]. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. (7) Verify that following function satisfies the hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x) = 2x2 - 4x +5, [-1, 3] (8) A population of the yeast cell Saccharomyces cerevisiae (a yeast used for fermentation) develops with a constant relative growth rate of 0.4159 per hour. The initial population consists of 3.8 million cells. Find the population size after 2 hours.(9) Use the curve sketching guidelines no sketch the following curve. HI) = (4 - 1')\" Domain: xintercept: yintercept: Symmetry: AsyEDpwtee: Intervals of Increase: Intervals of Decrease: Loon! Maximum: Local Minimums: Intervals of Concave Up: Intervals of Concave Down: Points of Inection: