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Simplify the expression.

$ \sin(\tan^{-1} x) $

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02:21

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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.

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00:53

01:11

Simplify the given express…

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02:02

Rewrite the expression as …

02:48

Let's find the sign of angers tension X So inverse tangent X means the angle Whose tangent is X and I'm gonna call that angle Fate up now let's draw picture. Suppose we have angle fatal here and we know it's tangent is X that means the opposite over adjacent is X. So if the opposite was X and the adjacent was one, that ratio would be X. Now, if that's the case, what's the length of the high pot news? If we're going to find the sine of the angle, we're going to need the high pot news as well as the opposite. So for now, I'm going to call the high pot news H. And now I'm going to use the Pythagorean theorem to find it. H squared equals one squared plus X squared. So H is the square root of one plus x squared. Okay, so now I confined the sign of angle fada. It would be opposite which is X over high pot news, which is square root of one plus X squared

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