The radius of a right circular cylinder is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time. ​

A ball is thrown straight down from the top of a 220-ft building with an initial velocity of –16 ft per second. The position function is . What is the velocity of the ball after 4 seconds? ​

Find the derivative of the algebraic function . ​

Find the slope-intercept equation of the line tangent to the graph of  when . ​

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,378 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places. ​

Find an equation of the tangent line to the graph of the function  at the point . The coefficients below are given to two decimal places. ​

A population of 350 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when . Round your answer to two decimal places. ​

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ , ​

Find  in terms of x and y given that. ​

Find  by implicit differentiation. ​ . ​