46 29. dx6 720x-7

We have to prove :

$\frac{d^6}{d{x}^6}{x}^{-1}=720x^{-7}$

We will use following formula for differentiation:

$\frac{d{x}^n}{dx}=n{x}^{n-1}$

Here, we have to differentiate $x^{-1}$ six times to prove the given condition.

So, differentiating $x^{-1}$ with respect to $\text{'}x\text{'}$, we get

$\begin{array}{rcl}\frac{d{x}^{-1}}{dx}& =& \left(-1\right)x^{-1-1}\\ & =& -x^{-2}\end{array}$