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$f(x, y, z)=100 x^{1 / 2} y^{1 / 3} z^{1 / 6},$ determine (a) $f(4,8,1),(\mathrm{b}) f(16,27,64)$

(a) 400(b) 2400

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 1

Functions of Several Variables

Partial Derivatives

Johns Hopkins University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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

01:29

$f(x, y, z)=2 x^{2}-3 x y^…

00:59

$f(x, y)=100 x^{1 / 4} y^{…

00:56

$f(x, y)=75 x^{1 / 3} y^{2…

01:01

$f(x, y, z)=100 \sqrt{x+2 …

00:58

$f(x, y)=x^{2}-y^{2}-3 x^{…

01:26

find $f_{x}, f_{y},$ and $…

03:13

All right. Um So we have a function in three variables. Um That means there's three inputs, we get one numbers and output. Um And we just want to figure out the value at these two points. Um So we're putting in four for x. Eight for y and one frizzy. So 100. We get four to the one half. 8 to the 1 3rd And 1 to the 1 6th. Those all get multiplied four to the one half is the root of four is 28. The one third is the cube root of eight which is also two and then one to the 161. So that's a total of 400. Let's do the same thing again. This time we're putting in 16 for X. 27 for Y. for Z. So 116 to the one half Times 27 to the 1/3. I am 64 to the 1/6. Okay, the square root of 16. S. Four. Key route of 27 is three. Sixth. Route of 64 is too you may not have known that but it is certainly welcome to use a calculator for these. If you don't know them. Get 2400

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