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Find the second derivative of the function . ​

Evaluate the derivative of the function at the point . ​

The volume of a cube with sides of length s is given by . Find the rate of change of volume with respect to s when centimeters. ​

Find an equation of the tangent line to the graph of the function given below at the given point.  , (The coefficients below are given to two decimal places.) ​

A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure). When he is 13 feet from the base of the light, at what rate is the tip of his shadow moving? ​ ​

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

Find the derivative of the function . Simplify your answer. ​

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. ​ ​

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? ​ ​

You are staining a Gram-negative bacterium and forgot the decolorization step (but continued with the rest of the procedure). What result do you expect at the end of the Gram stain?