Find the derivative of the function. ​ . ​

All edges of a cube are expanding at a rate of 7  centimeters per second. How fast is the volume changing when each edge is 2  centimeters? ​

An airplane is flying in still air with an airspeed of 283  miles per hour. If it is climbing at an angle of 21 °, find the rate at which it is gaining altitude. Round your answer to four decimal places. ​

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch). A model that approximates the data is . Find the rate of change of T with respect to p when . Round your answer to two decimal places. p 5 10 14.696 (1 atm) 20 30 40 60 80 100 T 327.43 404.29 448.84 485.71 536.18 573.59 629.02 670.61 704.38 ​

A point is moving along the graph of the function  such that  centimeters per second. Find  when . ​

Find if . ​

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level? ​ ​

Find an equation of the tangent line to the graph of  at the point . ​

Find the rate of change of the distance  D  between the origin and a moving point on the graph of  if   centimeters per second. ​

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. ​