Question

Find the rate of change of the distance between the origin and a moving point on the graph of y = x^2 + 1 if dx/dt = 2 centimeters per second.

Answer 1

Step 1:

The function is .

Consider moving point is .

Consider is the distance between the origin  and the point .

The distance between two points is .

Then

        

.

Substitute in above expression.

Step 2:

.

Apply derivative on each side with respect to .

Rewrite the expression.

Substitute in above expression.

.

Solution :

The rate of change of distance is .