Fuck me

Fuck me

How is this derived?

[math]f(x,y)=\sqrt{x^2-120x+y^2-50y+4225}[/math]

Hope my [math]\LaTeX[/math] isn't fucked.

I would love to help but your question has no context. You gave a function and ask how the function was derived. I have no starting point to work with.

This is an equation for a circle given a constant radius. Are you asking how to put this into standard form?

fucking rekt

Pick a variable, differentiate as normal treating the other variable as a constant. That's pretty much how you do partial differentiation.

In parts of Europe, people say derive instead of differentiate.

Fair enough. If this is true then he still has some ambiguity (as you mention) with respect to which variable.

If the goal is to differentiate, then lets do it with respect to [math]x[/math]:

[math]\frac{\partial}{\partial x}f(x,y) = \frac{\partial}{\partial x} \sqrt{x^2 - 120x + y^2 - 50y + 4225} [/math]
From the chain rule we know that to differentiate a function [math]u(x)[/math] we must compute
[math]\frac{\partial}{\partial x}u(x) = \frac{\partial u}{\partial t} \cdot \frac{\partial t}{\partial x} [/math]

where [math]t[/math] is a function of [math]x[/math] "inside" the function [math]u(x)[/math]. In this case we have that
[math]u(x) = f(x,y) = \sqrt{x^2 - 120x + y^2 - 50y + 4225}[/math]

where the "internal" function [math]t(x)[/math] is everything under the radical [math]t(x) = x^2 - 120x + y^2 - 50y + 4225[/math]

So, with these substitutions we can write
[math]\frac{\partial}{\partial x} f(x,y) = \frac{\partial f}{\partial t} \cdot \frac{\partial t}{\partial x} [/math]

Hence
[math] \frac{\partial f}{\partial t} = \frac{\partial}{\partial t} \sqrt{t} = \frac{1}{2\sqrt{t}} [/math] by the "power rule", and
[math] \frac{\partial t}{\partial x} = \frac{\partial}{\partial x} (x^2 - 120x + y^2 - 50y + 4225 ) = 2x - 120[/math]

Then, taking the product of our two intermediate derivatives we find our desired result
[math]\frac{\partial}{\partial x}f(x,y) = \frac{\partial f}{\partial t}\frac{\partial t}{\partial x} = \frac{1}{2\sqrt{t}} (2x - 120) = \frac{x - 60}{\sqrt{t}}[/math]

and recalling our substitution [math]t = x^2 - 120x + y^2 - 50y + 4225[/math] we find
[math]\frac{\partial}{\partial x}f(x,y) = \frac{x - 60}{\sqrt{ x^2 - 120x + y^2 - 50y + 4225}}[/math]

as desired.

Literally only Americans use "derive" and it sounds stupid, too.

>Literally only Americans

Nope Germans use it to, not sure if it's all Germans, but I know some do.

American here. Never heard it that way

Canadian here. I've only hear 'derive' to mean 'differentiate' in either informal contexts or contexts where it was there was absolutely no ambiguity where it meant to differentiate and not to generate a result.

I wouldn't say the two are interchangeable, but there's definitely some leniency

I'm American and I had it hammered into my brain that the word is "differentiate" and not "derive". It really fucking bothers me when people say derive when they mean differentiate, because derive already means something.

Yeah, I usually point it out just to be sure they mean differentiate if there's any possible ambiguity. In my experience professors rarely make this swap.

We use it in Germany...

> Germany

I assume you're taught mathematics in German.: So, is this a linguistic thing? Is there no distinction between the verb "to derive" and "to differentiate" for (at least) both meanings of the action of derivation?

we use it in france

we use it in italy

Let's break this down shall we?

f(x,y)=x2−120x+y2−50y+4225−−−−−−−−−−−−−−−−−−−−−−−√

f=finance
x=ex
y=why
x2=two times
-120=loss of 120 monies

basically the fiance says your ex was bad (why?) because that bitch stole -120 monies from you (like, two times) for some terrible math shit

don't go back to them user, they're no good if they steal ur monies

#mathiseasy

Can confirm. Frankfurt fag here, go to normal German school, every math teacher uses derive

Rofl.. Jesus christ I hate when people say, "derived," when they really mean "differentiated." To derive something is to obtain something from something. Derive what? How you do you derive the derivative? A derivative is a noun, not a verb, so it makes no sense to go changing the tense like that.. The action of finding a derivative is to differentiate. How do I differentiate this? How is this differentiated?

Frankfurt =/= School
Frankfurt = Antipositivism

you tried really hard to make that joke, didnt you?
it wasnt worth the effort

user what the fuck are you talking about, the econo-cucks live across the river.

I also had a professor that would say substract instead of subtract.

>I've only hear 'derive' to mean 'differentiate' in either informal contexts or contexts where it was there was absolutely no ambiguity where it meant to differentiate and not to generate a result.
You can't just use a completely unrelated word because it's an informal conversation and they will probably get what you mean.

Well we usually use "ableiten" for derivate and "herleiten" for derive

Same in French, to differentiate actually means a completely separate thing (différencier).

oh god what a retarded post

Literally no one in America says this dipshit. It's a European thing

I'm at an american university and I have an Indonesian professor who says this