- #1
Loberg
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Homework Statement
Can someone please check my working, as I am new to Einstein notation:
Calculate $$\partial^\mu x^2.$$
Homework Equations
3. The Attempt at a Solution [/B]
\begin{align*}
\partial^\mu x^2 &= \partial^\mu(x_\nu x^\nu) \\
&= x^a\partial^\mu x_a + x_b\partial^\mu x^b \ \ \text{(by product rule and relabelling indices)} \\
&=x^a\delta_\mu^a + x_b\delta_\mu^b \\
&=2x_\mu.
\end{align*}
I'm not sure is the expression in the second term of the second line is correct, as the partial is with respect to the covariant vector but the argument is a contravariant vector.