Question

Find the rate of change of the distance between the origin and a moving point on the graph of y = x²+1.

Answer 1

Let L be the distance between the origin and a moving point. I know that L = √(x² + y²).

How can I find the rate of change of L? Should I derivative it? In respect of what?

Answer 2

You know that \[y=x^2+1\] so you can have L(x) as the distance from the origin as a function of x...

Answer 3

presumably it's with respect to time...

d/dt (L= sqrt(x^2 + (x^2+1)^2))

or...
d/dt(L^2 = x^2 +y^2)
2L* dL/dt = 2x* dx/dt +2y* dy/dt

either way works..