maximum limit of 20 derived fields

There is no way around that limit.  The only option is to carefully review each form rule and see if you can re-write it in a way which does not "use up" a derived field.  A derived field is one which is a formula or a lookup, basically one that is not a simple data entry field.

In some cases, you may be able to have a more complex formula fieldbut fewer of them use in the form rules.  For example, if a form rule depends on two formula fields, and you can combine those two fields into a single field by formula for the purpose of a form rule.

>Is there any way to get around this limit?

Use script and you will not hit these arbitrary limits.

I don't know how to do that. Can you point me in the right direction? All I'm looking to do is show specific sections when it is a specific task. I have about 15 different scenarios for this.

Just to pile on some since you discuss limits, I have put in feedback, yes generic sounding, but specific to the entire QB program.  There are way too many QB imposed limits that don't need to be there.  Please follow this User Feedback link and vote to try and get QB to remove all the arbitrary limits they have imposed.
https://quickbase.uservoice.com/forums/111823-quick-base-product-feedback/suggestions/20014867-remove-arbitrary-limits-imposed-in-the-software

Thanks.

Thanks Neil!  I added votes to that post.

Here is another User Feedback link to requesting a removal of those pesky derived field limits.
I wish I could drop more than 3 votes for this idea, because it causes so much additional energy and time in building viable work-arounds!

https://quickbase.uservoice.com/forums/111823-quick-base-product-feedback/suggestions/5720434-increase-the-number-of-allowed-derived-fields