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. ​

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. ​ Find the rate of change of area, A, when the radius is 3. ​

Suppose a 20-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. ​

Evaluate  for the equation at the given point. Round your answer to two decimal places, if necessary. ​

Use implicit differentiation to find . ​ ​

Find the slope-intercept form of the equation of the line tangent to the graph of  when . ​

A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure). When he is 13 feet from the base of the light, at what rate is the tip of his shadow moving? ​ ​

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 . ​