- #1

- 254

- 5

## Homework Statement

Solve this, $$\frac{\partial}{\partial x^{\nu}}\frac{3}{(q.x)^3}$$

where q is a constant vector.

## Homework Equations

## The Attempt at a Solution

$$\frac{\partial}{\partial x^{\nu}}\frac{3}{(q.x)^3}=3\frac{\partial(q.x)^{-3}}{\partial (q.x)}*\frac{\partial (q.x)}{\partial x^{\nu}} \\ =\frac{-9}{(g^{\mu \nu}q_\mu x_\nu)^4}[g^{\mu \nu}[q_{\mu,\nu}x_{\nu}+q_{\mu}x_{\nu,\nu}]] \\ =\frac{-9}{(g^{\mu \nu}q_\mu x_\nu)^4}[g^{\mu \nu}[0+q_{\mu}x_{\nu,\nu}]] \\ =\frac{-9}{(g^{\mu \nu}q_\mu x_\nu)^4}[[q_{\mu}\delta^\mu _\nu]]\\ =\frac{-9}{(g^{\mu \nu}q_\mu x_\nu)^4}q_{\nu}$$

Is this correct? Besides is there an easier or faster way to solve this? Or can it be reduce further to lesser terms?

Last edited: