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I study mathematics-economics in the second year of a bachelor programme: I’m one month into the...

I study mathematics-economics in the second year of a bachelor programme: I’m one month into the course “Analysis I”. I would like to get more familiar with certain subjects. For a reasonable answer for this Q&A, I’d like a formal definition, a simple example/proof and summary of the mentioned subject.

The subject is the sum, product and composition of differentiable functions.

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