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Homework Statement
Homework Equations
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I believe that ##\frac{\partial x^u}{\partial x^p} =\delta ^u_p ## (1)
##\implies ## (if ##\delta^a_b ## is a tensor, I'm not sure it is?) : ##\frac{\partial x_u}{\partial x^p} = g_{au} \delta ^a_p ## (2)
The Attempt at a Solution
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sol attached:
because partial derivatives commute four of the terms cancel and I agree with the solution to get the remaining two terms the same, however, I have a delta in place where the solution has a metric so instead I would get(using (2)):
##g_{av}\delta^a_u \frac{\partial}{\partial x^p}g_{ap}\delta^a_u\frac{\partial}{\partial x^v} ##
Many thanks for your help.
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