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I have sort of a fundamental elementary calculus question. So, when trying to understand differentials, I always interpret is as change in the function corresponding to the change in the inputs. I always thought of these changes as "infinitesimal" changes and the differential for me was basically the change in function for an infinitesimal perturbation to its input. Is that interpretation correct?

I was browsing the wikipedia entry here (https://en.wikipedia.org/wiki/Differential_of_a_function) and it says that the modern interpretation of a differential is seen as the function of two independent variables x and [itex]\Delta[/itex] x. So essentially the differential depends on where it is computed (the value of x) and how much the value is perturbed by i.e. [itex]\Delta[/itex] x.

However, now the differential is not this "infinitesimal" quantity i.e. dy can be any real number depending on the product f'(x) * dx. Is that correct? Somehow I have thoroughly managed to confuse myself...

Many thanks for any help you can give me.

Luca

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# Understanding differentials

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