I need help with these four problems:

Problem #1:

For the function, find the indicated expressions. f(x) = In(ex - 2x) (a) Find f'(x). F'(x) = (b) Find f'(0). f'(0) =For the function, find the indicated expressions. f(x) = x6 In(x) - x6 (a) Find f'(x). f' (x ) = (b) Find f'(e). (Round your answer to five decimal places.) f'(e) =The weekiylr sales (in thousands) of a new product are predicted to be 5(x) - 800 700e'D'1" time. (Round your answers to one decimal place.) after x weeks. Find the rate of change of sales after the following amounts of (a) 1 week thousand sales per week (b) 13 weeks thousand sales per week The following function is a company's price function, where p is the price (in dollars) at which quantity x (in thousands) will be sold. p = 100e-0.5x (a) Find the revenue function R(x). [Hint: Revenue is price times quantity, p . x.] R(X) = (b) Find the quantity and price that will maximize revenue. (Round your answers to two decimal places.) X = thousand units P = $