Find  in terms of x and y. ​ ​

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

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. ​

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. ​

Find  by implicit differentiation given that . Use the original equation to simplify your answer. ​

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,372 feet tall. Determine the velocity function for the coin. ​

Find the slope of the graph of the function at the given value. ​ when ​

Use implicit differentiation to find . ​ ​

Use logarithmic differentiation to find . ​ ​

Find the derivative of the function . Simplify your answer. ​