## Tripping over a basic derivation

This is a classic example of how I get tripped up. What is wrong here? (Goldstein derivation 1.1)

Show that for a single particle with constant mass the equation of motion implies the following differential equation for the kinetic energy: while if the mass varies with time the corresponding equation is

I find the first just fine

The second, I got trapped

Is the right answer, but I trapped myself with

What is wrong? I used the *constant * relation found initially in the non-constant derivation!

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