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

$ f(x) = \ln (x^2 - 2x) $

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domain: $(-\infty, 0) \cup(2, \infty) $

00:56

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

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In this problem, we are given a function and we are asked to find derivative in the domain of this function. We'Re going to start from derivative prime of x will be 1 over x, squared minus 2 x times that union function, so that will then be 2 x, minus 2 divided by x, squared minus 2 x. We know that in order to find the domain in tint first know that argument of natural log should be positive, meaning an x paris to x should be positive, now x, square minus 2 x, i x times x, minus 2, and that should be positive, for this Has 2 roots 1 is 1 x is 0 and other 1 is 1 x. 2 point in order to, for this, 1 to be positive x should be less than 0. So it's positive here negative here and positive here so x should be in this interval and tenths interval. So we're going to say that the domain has negative infinity to 0 open interval union 2 to positive infinity, open interval.

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