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? ​

Use implicit differentiation to find  at the point. ​ ​

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

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. ​

Differentiate the function . ​

A spherical balloon is inflated with gas at the rate of 500  cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 40  centimeters? ​

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

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

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

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. ​ ​