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

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 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. ​

Find the second derivative of the function . ​

Evaluate the derivative of the function at the point . ​

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 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.) ​

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 of the graph of the function at the given value. ​ when ​

Find the derivative of the function . Simplify your answer. ​