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

$ u(t) = \dfrac {\tan t}{1 + \tan t} $

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01:22

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

Johns Hopkins University

Missouri State University

Harvey Mudd College

Baylor University

Lectures

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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's the function U of T and we want to think of the function as a composition f of G and another way to write that would be with parentheses, f of g of t. So, looking at it that way we can tell that G would be the inside function and f would be the outside function. So when we look back at V A. T what appears to be the inside function? What we can see that tangent t is on the inside of something else in two places. So we could say that GFT is tangent e So what is it inside of? So what is fft? Well, we would have to have tea on the top to place the g of t in there and we would have to have one plus t on the bottom to place a tangent of T in there, so that would be our FFT. So f of G would give us the original function

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