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$f(x, y)=2 x^{2}-3 x y^{2}-2 y^{3},$ determine (a) $f(2,-1),(\mathrm{b}) f(-1,2)$

(a) 4(b) -2

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^{…

01:29

$f(x, y, z)=2 x^{2}-3 x y^…

01:53

$$\text { If } f(x, y)=x^{…

00:43

$f(x, y)=4 x^{3} y^{2}$ de…

02:49

If $f(x)=x^{2}-3 x,$ find …

02:15

If $f(x, y)=x^{2} y /\left…

02:23

Find (a) $f_{x}(x, y),$ (b…

02:54

Find the specific function…

All right. We want to figure out the value of this multi variable function at these two points. Two comma negative one and negative one comma two. So we're just going to put in two for X. And negative one for why? So two times two squared here. I see an X. So I put it to I see why I put a negative one. There's only a why in the last term such as -1. All right. So that's a total of 8 -6. And then this is a plus because negative one cubed is negative two. So a total of four. Same thing for the second one. This time putting a negative one for X. And two for why? Um negative one for X and two for y -2 times two. Cute. Okay, so then I get positive too positive 12. Negative 16. So a total of -2.

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