Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = Vx (a) Find dy/dt, given x = 4 and dx/dt = 6. dy/ dt = (b) Find dx/dt, given x = 81 and dy/dt = 4. dx/dt =A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x. y = 2x2 + 1; dx = 4 centimeters per second dt (a) x =-1 cm/sec (b) X =0 cm/sec (c) x=1 cm/secA point is moving along the graph of the given function at the rate dx/dt. Find dy/dt (in ft/sec) for the given values of x. y = tan(x); dx = 6 feet per second dt (a) X= - 3 dy = ft/sec dt (b) X = - 4 dy = ft/sec dt (c) X = 0 dy = ft/sec dtThe radius r of a circle is increasing at a rate of 8 centimeters per minute. Find the rate of change of the area when r = 32 centimeters. cm2/minThe radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change of the volume when r = 8 inches. in.3/min (b) Find the rate of change of the volume when r = 38 inches. A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 30 centimeters and r = 55 centimeters. ,- = 30 cm/min r = 55 cm/min