If the length of a rectangle decreases at the rate of 3 cm/sec and its width increases at the rate of 2 cm/sec, find the rate of change of the area of the rectangle when its length is 10 cms and its width is 4cms. Let denote length, denote width and denote the area of the rectangle. Then by implicit differentiation

                                         
In particular, that is, the area of the rectangle increases at the rate of .

An airplane is flying in a straight path at a height of 6 Km from the ground which passes directly above a man standing on the ground. The distance of the man from the plane is decreasing at the rate of 400 km per hour when . We want to find the speed of the plane. To find this, let denote the horizontal distance of the plane from the man. We note that for . We are given that