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. ​

Given the derivative below find the requested higher-order derivative. ​ , . ​

Use implicit differentiation to find  at the point. ​ ​

A projectile is shot upwards from the surface of the earth with an initial velocity of 122 meters per second. The position function is . ​ What is its velocity after 3 seconds? ​