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

Find  in terms of x and y. ​ ​

Use logarithmic differentiation to find . ​ ​

Use implicit differentiation to find . ​ ​

Find the slope of the graph of the function at the given value. ​ 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 1,372 feet tall. Determine the velocity function for the coin. ​

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

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

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing? ​ ​

Find  in terms of x and y given that. Use the original equation to simplify your answer. ​