1.Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
y=2(x^2+3x)
a. Find dy/dt when x = 5, given that dx/dt = 5.
b. Find dx/dt when x = 6, given that dy/dt = 1.
2. Find the rate of change of the distance between the origin and a moving point on the graph y = sin(3x) ifdx/dt = 3 centimeters per second.
a. Let D be the distance between the origin and a moving point on the graph of y = sin 3x.
b. Substitute y = sin 3x in the formula for distance.D = x2 + y2
c. Differentiate D = x2 + sin23x with respect to t and simplify.