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Find by implicit differentiation given that . ​

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

A point is moving along the graph of the function  such that  centimeters per second. Findwhen . ​

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

Evaluate the derivative of the function at the point . ​

Find the second derivative of the function . ​

Find  at the point for the equation. ​

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

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? ​ ​