1.Assume thatxandyare both differentiable functions oftand find the required values ofdy/dtanddx/dt.

y=2(x^2+3x)

a. Finddy/dtwhenx=5, given thatdx/dt=5.

b. Finddx/dtwhenx=6, given thatdy/dt=1.

2. Find the rate of change of the distance between the origin and a moving point on the graphy= sin(3x)ifdx/dt=3centimeters per second.

a. LetDbe the distance between the origin and a moving point on the graph ofy= sin3x.

b. Substitutey= sin3xin the formula for distance.D= x²+y²

c. DifferentiateD=x²+ sin²3x

with respect totand simplify.