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Express the function in the form $ f \circ g $.

$ v(t) = \sec (t^2) \tan (t^2) $

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01:30

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

Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

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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.

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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.

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here we have a function V of tea and we want to think of V A. T as a composition of functions f of G and another way to write that would be f of G of tea with parentheses. And looking at that notation, we can see that g of t is the inside function and f of tea is the outside function. So thinking about it that way we could see that the inside function could be t squared so we could let g of t equal t squared. And so the outside function would be C can't t tangent t And that way, if we found f of G, we could substitute t squared in for tea and we would get the original function v of tea.

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