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Problem

If $ f(x) = \ln (x + \ln x), $ find $ f'(1). $

00:56

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Problem 30 Easy Difficulty

Differentiate $ f $ and find the domain of $ f. $

$ f(x) = \ln \ln \ln x $


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01:31

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Related Topics

Derivatives

Differentiation

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Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Video Transcript

in this trouble working in the function were first has to find Derek off dysfunction. And then we're asked by the domain of dysfunction, we're gonna start from Veritas. Five banks will be So we have seen actual love. We're gonna start from outward and then moves to the internal. So we gonna have won over natural law. Natural. Thanks. Multiply by gravity. Oh, action! Log up. Next level X. That is what Over nature, Law, nation Look affects time salute our nation local Thanks. What's a black by? There is a au natural x Primal backs is equal to one over X It comes from here Times National log of X is disturbed Time station log off Next level There's all right now we want to decide on the domain We have three natural lots again satisfying this or making this define is not you know you want to make sure that this after national law as before So we don't have been in order for that. In order for this after nation locked be defined. We know that this argument right here financial log off natural local tax should be positive in order for that want to be posted. It means that the actual log of X should be greater than world, so this should be greater number. Just satisfy this. We don't know that X should be rated that he so domain is than all the numbers for a positive impunity opening toe.

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Calculus: Early Transcendentals

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Related Topics

Derivatives

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Top Calculus 1 / AB Educators
Catherine Ross

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Anna Marie Vagnozzi

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Heather Zimmers

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Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
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