I attended the Calculus course at my university, but neither I or my colleagues could understand what “exactly” is dx and its purpose. Thanks!
In: Mathematics
It’s more of a reference point than anything else, to my understanding it’s to help you know which variable you’re integrating or deriving, and is most useful in equations with multiples different variables. So for instance, if you have an equation where f(x)=3xy , the derivative would be dx=3y because the it’s the derivative of the function with respect to x
Intuitively, it’s a very small change in x.
The derivative (dy/dx) is a measure of how much a small change in x affects y. That’s why it’s written as a fraction of two very small numbers, dy and dx.
The integral can be seen as a sum of areas of very thin rectangles. The height of each rectangle is the value of the function f(x), and the width is some small change in x, so we write it as Integral f(x) dx.
The “d” refers to the delta of x. But not just any delta; it’s only written as “d” when we’re talking about the delta as it approaches zero — or is infinitely small. So you can think of it as x at a single point along the function.
X is the variable you’re integrating.
For example, if your problem is integrating with respect to time it could dt.
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