I want the answer to be CLEAR and EASY TO FOLLOW not handwritten on a notebook but it's okay if you handwrite it on the picture I'm submitting

Calculate the derivatives of the following functions. (10 points each) (a) F(x) = (x? 1), F10x) = (b) g(x) = e*sin(4x) g'(x) = 3) Use implicit differentiation to find g for the following equation. (10 points) 1y=4-x% 4) Find the point in the given domain where each function satisfies the MVT. If there is no point choose one of the choices: (5 points each) (A) The function is not continuous on [a, b] (B) The function is not differentiable on (a, b) @y =x% [-12] by== [-22] 5) (8 points) As a pot of tea cools, the tea is modeled by a differentiable function H for 0 =t = 10, where time t is measured in minutes and temperature H(t) is measure in degrees Celsius. Values of H(t) at selected values of time t are shown in the table below. H(t) (C) Use the data in the table along with the Mean Value Theorem to approximate the rate at which the temperature of the tea is changing at time t = 3.5. Show the computations that lead to your answer and interpret its meaning in the context of the problem. (6) Use a linear approximation to approximate +23. (10 points) Lix) = V73 =