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

(a) 3(b) -77

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

00:59

$f(x, y)=2 x^{2}-3 x y^{2}…

00:47

$f(x, y)=2 x y-3 x^{2} y^{…

01:29

$f(x, y, z)=2 x^{2}-3 x y^…

03:05

If $f(x)=\frac{2 x-3}{3 x+…

01:13

For $f(x, y)=2^{x}-3^{y},$…

00:50

$f(x, y)=x / y,$ determine…

02:54

Find the specific function…

00:37

Find $f_{x}$ and $f_{y}$ w…

01:57

All right. Um We have this function in two variables and we're just putting in values for X and Y. So if you want to find f of one comma negative one, we put in a one for X And then a negative one for why? Be careful? We need to square the entire negative one minus three times X is positive one. Why is negative one like that? Okay, so a total of 1 -1 Plus because we have a negative and a negative one here. three. So that's a total of three. Ok. For f of two comma three. Same thing to for X three for why? three times 2 cubed Times three. So that's gonna be kind of big. This is 4 -9 -9 times eight is 72. So we have a total of -77.

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