How exactly does deriving a profit function result in giving profit margin?

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How exactly does deriving a profit function result in giving profit margin?

In: Mathematics

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A margin is the incremental increase in some value. The derivative of the profit function will show you how much your income changes as you increase X, which might be investment into a certain technology or market sector. Since it shows how much your profit is changing, it shows you the margin for your profit as you increase investment: profit margin.