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Find the second derivative of the function. ​ ​

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. ​

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? ​ ​

Find the slope  of the line tangent to the graph of the function at the point . ​

A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 19 feet from the wall. Round your answer to three decimal places. ​ ​

Find  at the point for the equation. ​

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. ​

Find  if . ​