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

Answer 1

if the distance is s,

s^2 = x^2 + y^2

2s ds/dt = 2x dx/dt + 2y * 2x dx/dt
2s ds/dt = (2x^2 + 2x + 2) dx/dt
s ds/dt = (x^2+x+1)(2)

ds/dt = 2(x^2+x+1)/sqrt(x^4 + 3x^2 + 1)

If you know x, plug it in