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. ​

Evaluate the derivative of the function at the point . ​

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

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

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

When satellites observe Earth, they can scan only part of Earth’s surface. Some satellites have sensors that can measure the angle θ shown in the figure. Let h represent the satellite’s distance from Earth’s surface and let r represent Earth’s radius. Find the rate at which h is changing with respect to θ when (Assume miles.) Round your answer to the nearest unit. ​ ​

Find the second derivative of the function. ​ ​

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. ​

Differentiate the function . ​

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? ​