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$f(x, y)=x / y,$ determine (a) $f(3,2),(\text { b) } f(2,3),(\text { c) } f(x+h, y)$

(a) $3 / 2$(b) $2 / 3$(c) $\frac{x+h}{y}$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 1

Functions of Several Variables

Partial Derivatives

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

00:47

$f(x, y)=2 x y-3 x^{2} y^{…

00:58

$f(x, y)=x^{2}-y^{2}-3 x^{…

00:43

$f(x, y)=4 x^{3} y^{2}$ de…

00:44

Find $f_{x}$ and $f_{y}$

00:51

00:41

$$\text { Find } f_{x}, f_…

01:37

Given that $f(x)=2|x|+3 x$…

00:59

$f(x, y)=2 x^{2}-3 x y^{2}…

So we have a function in two variables and we want to find its value at all of these points. Um So let's start with three comma two, we're just putting in three for X and two for why? So this actually works out to just 3/2. And then now we're putting in two for X. And three for why? So this is to over three and then here this is a little tricky. We're putting an X plus H. Four X and Y. For why? So every time we see an X we write expose H. Every time we see why? Which is right? Why? So this case would be X plus H over why? It's a little weird but you can put functions are expressions with variables in there, you can have the variable itself modify it. Um And what this is doing is it's getting us ready to calculus, we see an explicit age here. So we're going to be able to derive calculus formulas with functions of multiple variables.

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