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ehrenfest
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Homework Statement
Zwiebach QC 6.4
Why is
[tex] \frac{\partial}{\partial{X^{\mu}}} \left( \frac{\partial X}{\partial{\tau}} \cdot \frac{\partial X}{\partial{\sigma}} \right) ^2 = \left( \frac{\partial X}{\partial{\tau}} \cdot \frac{\partial X}{\partial{\sigma}} \right) \cdot \frac{\partial{X^{\mu}}}{\partial{\tau}}[/tex]
The dot is the relativistic dot product.
What I am confused about is how you take the derivative with respect to one component X^mu of the spacetime vectors and get a quantity that still has [tex] \left( \frac{\partial X}{\partial{\tau}} \cdot \frac{\partial X}{\partial{\sigma}} \right) [/tex]. Is there an intermediate step someone could show me?
Homework Equations
The Attempt at a Solution
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