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Find the rate of change of the distance  D  between the origin and a moving point on the graph of  if   centimeters per second. ​

The radius  r  of a sphere is increasing at a rate of 2  inches per minute. Find the rate of change of the volume when  inches. ​

Suppose a 20-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. ​

Use logarithmic differentiation to find . ​ ​

Evaluate  for the equation  at the given point . Round your answer to two decimal places. ​

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 1,372 feet tall. Determine the velocity function for the coin. ​

A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure). When he is 13 feet from the base of the light, at what rate is the tip of his shadow moving? ​ ​

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

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. ​

Find the second derivative of the function . ​