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. ​

Use the rules of differentiation to find the derivative of the function . ​

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the velocity of the object when . Round your answer to two decimal places. ​

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. ​ ​

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is . ​ What is its velocity after 3 seconds? ​