# Derivatives on tensor components

#### RicardoMP

Problem Statement
I want to prove that $$-\frac{\partial}{\partial p_\mu}\frac{1}{\not{p}}=\frac{1}{\not{p}}\gamma^\mu \frac{1}{\not{p}}$$
Relevant Equations
$$\not{p}=\gamma^\mu p_\mu$$
This was my attempt at a solution and was wondering where did I go wrong: $$-\frac{\partial}{\partial p_\mu}\frac{1}{\not{p}}=-\frac{\partial}{\partial p_\mu}[\gamma^\nu p_\nu]^{-1}=\gamma^\nu\frac{\partial p_\nu}{\partial p_\mu}[\gamma^\sigma p_\sigma]^{-2}=\gamma^\nu\delta^\nu_\mu\frac{1}{\not{p}^2}=\gamma^\mu\frac{1}{\not{p}^2}$$
Any hint would be great! Thank you!

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#### samalkhaiat

Apply the Leibniz rule to $$\left( \frac{\partial}{\partial p_{\mu}} \frac{1}{\not\! p} \right) \not \! p \ .$$

"Derivatives on tensor components"

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