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

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01:59

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Missouri State University

Campbell University

Harvey Mudd College

University of Nottingham

Lectures

04:40

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.

44:57

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.

15:49

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02:29

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00:52

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01:01

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02:56

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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