Like, x squared plus y, but it could also output a vector, right? So you could also imagine something that's got multivariable input, f of x, y, and it outputs something that also has multiple variables, like, I mean I'm just making stuff up here, three x and, you know, two y. Number that depends on x and y in some way, Commonly it will output just a number, so you might imagine a

What letters to use, and it could be, you know, x, y, z, x one, x two, x three,Ī whole bunch of things, but just to get started, we often think just two variables and this will output To write it as x, y, it doesn't really matter So then a multivariable function is something that handles Some kind of number as their input, and then the output is Ordinary calculus world, will have a single input, You're about to study? Well, I could say it's allĪbout multivariable functions, that doesn't really answer anything because what's a multivariable function? And basically, the kinds of functions that we're used to dealing with, in the old world, in the So, the first thing we gotta get straight is what is this word multivariable that separates calculus, as we know it, from the new topic that

Of things when applicable, and boy, is that applicable when it comes to multivariable calculus. I am, sadly, not Sal, but I'm still gonna teach you some math. So I think I should probably start off by addressing the elephant Hello and welcome to multivariable calculus.

Khan academy multivariable calculus