Consider the following functions. g(x) = 6x2 - 4 h(x) = v 6x2 -. 8 f(x) = 6x - 4 Find the derivative of each function. g ( x) = h( x) = f' (x) =Continuing Education Enrollment The registrar of a certain university estimates that the total student enrollment in the Continuing Education division will be given by 15,000 N(t) = - + 19,000 V1 + 0.1t where N(t) denotes the number of students enrolled in the division t years from now. Find an expression for N'(t). N'(t) = How fast will the student enrollment be increasing 2 years from now? (Round your answer to the nearest integer.) students per yr How fast will it be increasing 8 years from now? (Round your answer to the nearest integer.) students per yrAging Population The population of Americans age 55 and older as a percentage of the total population is approximated by the function t) = 10.72019: + 10)'13 (o s t 3 20) where fis measured in years, with f = U corresponding to the year 2000i At what rate was the percentage of Americans age 55 and older changing at the beginning of 2007? (Round your answer to four decimal places.) At what rate was the percentage of Americans age 55 and older changing in 2017? (Round your answer to four decimal places.) What was the percentage of the population of Americans age 55 and older in 2017? [See Note on page 168. Round your answer to two decimal places.) :|% Coneider the following. x+ 1)2 x3 x} = ( Find the derivative of the function. Find the slope m of the line tangent to the graph of Ex} at the point (F, 4}. an: Find an equation of the tangent line to the graph of Ex} at the point {I 4}. E dy du dy Find and when y and u are defined as follows. du dx dx U = 5x - 6x2 dy = du du = dx dy = dx