Economics Textbook Help

Question

The problem I am working through deals with taking the derivative of $N^*$ with respect to tau:

I have the answer but can not seem to arrive at it.

Answer 1

$N^* = \left(1+\frac {\theta}{1-\alpha} + \frac {\theta\alpha\beta\delta}{(1-\alpha)(1-\tau)(1-\beta - \delta\beta)}\right)^{-1}\\ \frac {dN^*}{d\tau} = -\left(1+\frac {\theta}{1-\alpha} + \frac {\theta\alpha\beta\delta}{(1-\alpha)(1-\tau)(1-\beta - \delta\beta)}\right)^{-2}\left(\frac {\theta\alpha\beta\delta}{(1-\alpha)(1-\tau)^2(1-\beta - \delta\beta)}\right)$

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