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? ​

A spherical balloon is inflated with gas at the rate of 500  cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40  centimeters? ​