I just think of the definition of a derivative.

d is just an infinitesimally small delta. So dy/dx is literally just lim (∆ -> 0) ∆y/∆x. which is the same as lim (x_1 -> x_0) [f(x_0) - f(x_1)] / [x_0 - x_1].

Note: ∆ -> 0 isn’t standard notation. But writing ∆x -> 0 requires another step of thinking: y = f(x) therefore ∆y = ∆f(x) = f(x + ∆x) - f(x) so you only need ∆x approaching zero. But I prefer thinking d = lim (∆ -> 0) ∆.

I think it might be the wrong way around: Engineers like to use j for imaginary numbers because i is needed for current.

Mathematicians are taught to be elastic with notation, because they tend to be taught many different interpretations of the same theory.

On the other hand engineers use more strict and consistent notation, their classes have a more practical approach.

Using the same notation makes it faster to read and apply math, a more agile approach helps with learning new theories and approaches and with being creative.

An integral is usually written like ∫ f(x) dx or alternatively as df(x)/dx. Please note that this is just a way to apply the operation ‘Integration’, like + applies the operation ‘Addition’. There is no real multiplication or division.

But sometimes you can take a shortcut and treat dx as a multiplied constant. This is technically not correct, but under the right circumstances lands you at the same solution as the proper way. This then looks like this ∫ f(y) dy/dx dx = ∫ f(y) dy

Another thing you can do is to move multiplicative constants from inside the Integral to in front of the Integral: ∫ 2f(x) dx = 2 ∫ f(x) dx. (That is always correct btw)

What anon did was combine those two things and basically write ∫ f(x) dx = dx ∫ f(x). Which is nonsensical, but given the above rules not easily disproven.

This is more or less the same tactic used by internet trolls just in a mathy way. Purposefully misinterpreting arguments and information, that cost the other party considerably more energy to discover and rebut. Hence the hate fuck.

Integrals are an expression that basically has an opening symbol, and an operation that is written at the end of it that is used also as a closing symbol, looks kinda like:$ {some function of x} dx.

The person basically said “the dx part can be written at the start also, and that would make my so mad :3”: $ dx {some function of x}.

This gets their so mad because understandably this makes the notation non-standard and harder to read, also you’d have to use parentheses if the expression doesn’t just end at the function.

Note: dollar used instead of integral symbol

Hate ****

I too take hate shits on the toilet.