Find  in terms of x and y given that. Use the original equation to simplify your answer. ​

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 5 feet from the base of the light, at what rate is the length of his shadow changing? ​ ​

Differentiate the function . ​

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the position of the object when . Round your answer to two decimal places. ​

Use logarithmic differentiation to find the derivative of . ​

Identify the graph which has the following characteristics. , ​ Graph 1 ​ ​ Graph 2 ​ ​ Graph 3 ​ Graph 4 ​ ​

An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider θ and x as shown in the following figure. Write θ as a function of x. ​ ​

Find an equation of the tangent line to the graph of  at the point . ​

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

Use the alternative form of the derivative to find the derivative of the function at . ​