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Problem

Find $ \frac {d^9}{dx^9}(x^8 \ln x). $

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Problem 53 Medium Difficulty

Find a formula for $ f^{(n)}(x) $ if $ f(x) = \ln (x - 1). $


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01:59

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

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Derivatives

Differentiation

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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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Watch More Solved Questions in Chapter 3

Problem 1
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Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56

Video Transcript

uh, trouble were given a collection effects as nature love explains what you're arrested, fined and ordered their bitter, uh, dysfunction. All right, Lester quality first. Very quiet moments. Now, knowing that perfect is natural explains when we see that affects it will explain us what we can write this one as X minus one in earth. Now let's look at the second order. Derivatives that double prime of X B negative born times X minus fallen negative too. Now, first order their best people. Probable effects would be negative. One has negative two times x once one too negative. Third forward and F or X 40 Negative on negative too negative. Three comes excellence for pretty negative for power. I think we see the pattern here. So we're trying to find and all ex. Okay, one be ordered off. Decorative is off. As you can see from here, the term get is positive when the order for there to this, even the term we get For the devotee of the sign, both the director is negative. So we can I first not oneness, negative or power and plus fall so that all terms will be positive for negative. Also As you can see when it is the second order, inevitably have negative. All order would give us going to one time. Say headed to court order is for time to Time Street. So we're gonna have a minus form pictorial. And here we have explained this form to the end. Follow. We can right then from this F and 40 Gavito X has negative one Kirsten plus one off. Bye bye. And mind school factorial you wanted by X minus war to the end How?

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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

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

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
Recommended Videos

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Find a formula for $ f^{(n)}(x) $ if $ f(x) = \ln (x - 1). $

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Find a general formula for $f^{(n)}(x)$. $$ f(x)=(x+2)^{-1} $$

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