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Find $ f \circ g \circ h $.
$ f(x) = \tan x $ , $ g(x) = \dfrac{x}{x - 1} $ , $ h(x) = \sqrt[3]{x} $
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01:26
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 3
New Functions from Old Functions
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Harvey Mudd College
University of Nottingham
Idaho State University
Boston College
Lectures
04:31
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
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.
01:21
Find $f \circ g \circ h$
00:41
$\text { Find } f \circ g …
00:43
03:09
here we have the functions F, g and H, and we're going to find the composition f of G of h. Another way to write that is with parentheses, f of G of h of X. And when we read it that way we can see that H is the inside function. It's going to be substituted into G. So we're going to take the cube root of X and we're going to substituted into G. In both places, we see an X that gives us G of h of X. So G of h of X is the cube root of X over the cube root of X minus one. So that whole thing goes inside of death. So we take that whole thing and we substituted in to the F function in place of X. And that's going to result in the tangent of that Hubert of X, over the cube root of X minus one
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