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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. ​

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

Use logarithmic differentiation to find . ​ ​

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. ​

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. ​

Assume that  x  and  y  are both differentiable functions of  t.  Find  when and  for the equation. ​

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

The volume of a cube with sides of length s is given by . Find the rate of change of volume with respect to s when centimeters. ​

Find by implicit differentiation given that . ​

Find  by implicit differentiation given that . Use the original equation to simplify your answer. ​