->ds/dt where s is the arc length in cartesian coordinates is ((dx/dt)^2+(dy/dt)^2)^(1/2).(adsbygoogle = window.adsbygoogle || []).push({});

-> Therefore by the chain rule ds/dt = ds/dp * dp/dt, but if I substitute dx/dt=dx/dp* dp/dt and dy/dt= dy/dp* dp/dt in the formula above, I get ds/dt=ds/dp * |dp/dt|??

What is happening?

->Even by elementary thinking, ds/dt and ds/dp are always positive whereas dp/dt need not always be. So, how is the chain rule being followed here?

Please explain. I have spent a full evening thinking over this.

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# Chain rule violated for arc length?

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