How can I calculate the derivative of the following function w.r.t $x$
$$f(x)=\log_2(1+W(ax))$$
where $W$ is the lambert function.
2026-03-24 20:30:47.1774384247
derivative of log-lambert function
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$$f(x)=\log_2(1+W(ax))=\frac{\log (1+W(a x))}{\log (2)}$$ $$f'(x)=\frac{1}{\log (2)}\, \frac{W'(ax)}{1+W(a x)}$$ Since $$W'(t)=\frac{W(t)}{t (1+W(t))}$$ then $f'(x)=\cdots \,\,???$