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$f(x, y)=100 x^{1 / 4} y^{3 / 4},$ determine (a) $f(1,16),(\text { b) } f(16,81)$.

(a) 800(b) 5400

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

00:43

$f(x, y)=4 x^{3} y^{2}$ de…

01:05

$f(x, y, z)=100 x^{1 / 2} …

00:58

$f(x, y)=x^{2}-y^{2}-3 x^{…

00:56

$f(x, y)=75 x^{1 / 3} y^{2…

01:51

$y=f^{-1}(x)$ As $g^{\prim…

02:39

Given the function $f(x)=4…

00:59

$f(x, y)=2 x^{2}-3 x y^{2}…

01:53

$f(x)=\frac{4}{x^{2}+1}, \…

alright for these problems um we have a function in two variables and we just want to put in the values for the two variables. To figure out the value of the function at a point. So we're putting in one for X and 16 for why? So it's 100 we take one to the power of one quarter times 16 to the power of three quarters, so that's 100 times one times 16 to the power of one quarter is the fourth root of 16. So it's too, and then we have two cubed so we can take it to the quarter cube. You can also do this with a calculator but um It is possible to do without, so that's 800. And then for the second one, same thing, we put in 16 for X and 81 for Y. And they didn't choose those numbers of accidents. So 60 into the one quarter we said was to fourth root of 81 is three, so two times three cubes three cubed, just 27. So this is 50 400. There

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