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$f(x, y)=75 x^{1 / 3} y^{2 / 3},$ determine (a) $f(8,1),(b) f(27,8)$

(a) 150(b) 900

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

00:58

$f(x, y)=x^{2}-y^{2}-3 x^{…

00:43

$f(x, y)=4 x^{3} y^{2}$ de…

00:59

$f(x, y)=100 x^{1 / 4} y^{…

$f(x, y)=2 x^{2}-3 x y^{2}…

01:05

$f(x, y, z)=100 x^{1 / 2} …

00:47

$f(x, y)=2 x y-3 x^{2} y^{…

04:46

(a) Find $d y$ if $y=\frac…

00:37

Find $f_{x}$ and $f_{y}$ w…

01:44

Multiple Choice In Exercis…

for these problems, we just want to find the value of the function at these given points, Its function of two variables. So we just want to sub both of them in. So we're putting eight in for X. That gets raised to one third and we're putting one in for y. And that gets raised to the two thirds. So this is 75 times eight to the one third is the cube root of eight is too. Um And then one to the two thirds. Just one. So a total of 150 for the first one. And then we want to do the exact same thing we're putting in now. 27 to the one third. 27 for X. And eight for y. Okay, Cube Root of 27. No not a 27 cube root of 27 is three. Cube root of eight is too but it's two thirds now, so it's two squared. So we want four. And let's multiply this smartly four times 75 is 300 Times three is 900.

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