How would I solve this?

Find the rate of change of the distance between the origin and a moving point on the graph of y-sinx if dx/dt =2cm/sec when x= pi/2

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- Oct 24th 2009, 04:15 PMsupaflyz88Math help: rate of change?
How would I solve this?

Find the rate of change of the distance between the origin and a moving point on the graph of y-sinx if dx/dt =2cm/sec when x= pi/2 - Oct 24th 2009, 04:22 PMadkinsjr
- Oct 24th 2009, 04:47 PMadkinsjr
Ok, this is what you're looking for:

Use the distance formula:

$\displaystyle s=\sqrt{(x-0)^2+(sin(x)-0)^2}=\sqrt{x^2+sin^2(x)}$

Now find the derivative with respect to x: $\displaystyle \frac{ds}{dx}$ and find it's value at the given point. Then just use the chain rule:

$\displaystyle \frac{ds}{dt}=\frac{ds}{dx}\frac{dx}{dt}$