derivarite of inverse of complex function

Hello , i have a function as shown bellow

syms x
Y=1./(log(x)-1)
fplot(finverse(Y),[5,6])

We have made an inverse by using finverse(Y)

how do i differentiate this function?

"diff" is not working because when i comprare the values of diff with the finverse slope , it gives me a tottaly different result.

in symilar problem i used "polyder" function at it worked great, but here we need to make a derivatite on inverse of Y=1./(log(x)-1) which is far from being polynomial.

What could be done?

Thanks.