Assume that  x  and  y  are both differentiable functions of  t  . Find  when  and  for the equation. ​

Find the points at which the graph of the equation has a vertical or horizontal tangent line. ​ ​

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. ​

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? ​

A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write  as a function of x. ​ ​

In a free-fall experiment, an object is dropped from a height of 144 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 . Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places. ​ ​

If the annual rate of inflation averages over the next  years, the approximate cost  of goods or cervices during any year in that decade is where  is the time in years and  is the present cost. The price of an oil change for your car is presently. Estimate the price years from now. Round your answer to two decimal places. ​

Find the derivative of the function .  ​

A conical tank (with vertex down) is 12  feet across the top and 18  feet deep. If water is flowing into the tank at a rate of 18  cubic feet per minute, find the rate of change of the depth of the water when the water is 10  feet deep. ​

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? ​ ​