Using the shunting yard algorithm and postfix evaluation, can we get the derivative of a function?

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I'm trying to build a basic differentiation calculator and I've found some resources online stating that using postfix / RPN notation, it is possible to find the derivative of a function, but the resources are poorly documented and I couldn't find more information about it.

I'm building it using C# and it's simply meant to be a console app, I've been able to convert a function into postfix so far, including trig functions but I'm not sure how to proceed in terms of evaluating the postfix notation and getting the derivative if that's even possible using such method. Any help would be appreciated!

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