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I have been using, for the most part, the prime notation when I want to indicate differentiation. As off recently, I have gained more insight into Leibniz's notation. This triggered the following question: how does the prime notation indicate what we are differentiating with respect to? I immediately thought that the answer to my question is: whatever number goes in between the brackets e.g. f'(u) is the derivative of f with respect to u.

Is that accurate?

Thanks!