# Why does physicist cancel out differentials?

Why does physicist cancel out differentials?

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It just werks

B-but, I just need a demonstration.

he needs to see things in order to believe them
Why don't you have faith, brother?

chain rule

infinitesimals

y = mx
dy/dx = y/x = m
Mathfags btfo

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faith
So show me the fuckin axiom that let 'em cancel out differentials, I even saw them multiply by dx/dx like if that was a 1 i mean wtf

dx/dx like if that was a 1
Why would dx/dx not be unity? Shouldn't it be a pretty fundamental property of differentiation?

Because it works and it's easy to remember.

Change of variables, chain rule.

It's not an axiom, it's a set of theorems.

Usually 'dx' is used in a symbolic way, it's not a number. That's the reason it seems weird when you use it like a number (dividing), but it works because of more profound reasons.

it's a set of theorems.
Which ones?

because of more profound reasons
What reasons?

chain rule

It's basically chain rule, you could read Calculus from M. Spivak for further details.

Also, remember that it doesn't work with partial derivatives: theshapeofmath.com/oxford/physics/year1/calc/sepdiff

Usually 'dx' is used in a symbolic way, it's not a number.
I know, but 'dx/dx' is unity and does not require interpretation of 'dx' as a number, and is not a wrong statement. Of course you can't just cancel out 'dx'.

$F(x, y) = 0$
$\displaystyle \frac{\frac{\partial{F}}{\partial{x}}}{\frac{\partial{F}}{\partial{y}}} = -\frac{dy}{dx}$

This triggers the physishit

"cancelling out" differentials can be formally correct (for example in language of differential forms), so it's not like they're totally wrong. It also just werks, it's not correct the way physicists do it, but it can be treated as mnemonics for valid techniques. And we have to remember physicists are just dirty, dog eating animals and they don't do mathematics, they just try to apply the maths (but only the parts they remember and are not too hard) untill they theory works

physicists don't do mathematics
*A Physicist who won a Fields medal blocks your Path integral*

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think of 3 cogwheels connected,
x, y & z
and their turning speeds
dx/dt, dy/dt and dz/dt

*a mathematician who knows physics blocks your path integral*
ftfy

en.m.wikipedia.org/wiki/Edward_Witten
Edward Witten (/ˈwJtən/; born August 26, 1951) is an American theoretical physicis
*teleports the goalposts back*
pshh....... nothin personnel kid

This. On a Riemannian manifold $M$ the tangent space $T_xM$ at any $x \in M$ is spanned by $\partial_\mu$ whose dual basis in the cotangent space $T^*_xM$ is $dx^\mu$ such that $dx^\mu(\partial_\nu) = \delta_{\mu}^{\nu}$.

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Even mathematicians use this heuristics when solving problems as it's completly useless to through the formalism when you are trying to solve a harder problem. Research doesn't has a an end of chapter list of problems.

Phenotype Guy as a proof that physicists know maths is just like Maria Curie being a proof that women are good at science

Dividing by zero doesn't trigger physicists, it just makes you look retarded.

t. Brainlet.

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