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

Find by implicit differentiation given that . ​

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.) ​

Assume that  x  and  y  are both differentiable functions of  t.  Find  when and  for the equation. ​

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? ​

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? ​ ​