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 . ​

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. ​