Perform Calculation Depending On Cell Value

I'm developing a financial spreadsheet.

I've got a cell "Taxable Income" and another cell "Tax on Taxable Income" in sheet2.

When I enter a value in "Taxable Income" I want "Tax on Taxable Income" to automatically calculate based on formulas in sheet1. I don't know how to get "Tax on Taxable Income" to determine which formula to apply from the different tax brackets.

For example:
If taxable income is <$18201, tax = $o
If taxable income is between $18201 and $37000, Tax on Taxable Income =0.19*Taxable Income
If taxable income is between $37001 and $80000, Tax on Taxable Income =3572+0.325*(Taxable Income - $37000)

The idea behind having formulas in a different sheet is so over time when tax rates/brackets change I only have to change the formulas on one sheet.

I know how to use basic AND, IF statements e.t.c but I can't seem to get the syntax right for this to work.