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I am an engineering student that has recently taken it upon myself to try and pickup some math skills in my own time. When reviewing the concept of a differential I was a little bit lost. To be honest I don't understand exactly what it is, or what it could be "good for". IE how to apply it.

The book gives its definition of dy/dx = f'(x). Well what exactly

*is*dy, and dx? Most problems seem to be involved with calculating percentages of errors, but what in general does a differential solve?

Also the book I'm reading keeps bringing up dx in integration by mentioning (don't you remember this from differentials). Well yes I remember seeing it, but now I don't understand why it is appearing in integration. If anybody can explain this to me I'd appreciate it. I feel like I only know the mechanical steps of differentiation/integration and didn't really understand what half this stuff was actually doing.