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Find $ f'(x). $ Check that your answer is reasonable by comparing the graphs of $ f $ and $ f'. $$ f(x) = \arctan (x^2 - x) $

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00:25

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

Oregon State University

Baylor University

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.

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in this problem. We're giving affliction effects and were asked to find Geritol this function of private pigs. Let's do that. Be Owner David are negative. X is one of our experts. Oregon. Use that form of X will then be on over one plus experience minus X squared times. David talked e inter function where your functions experiments Eso looks like my beady eggs off experiments X We don't find that there were two as two X minus one you wanted by one waas ex crate by specs. Quiet weekend. Burgess sent fighters. Now we asked a graphic effects in a primal Next. You see that this blooper is a perfect and threat curves perfects doesn't make sense. Well, yes, it actually does. As you can see, up to this point, the function is almost constant. So that's why we have here zero their bitter. So it means that RG Carlson and dysfunction at this boy is increasing writer up to this point, and here be they reject changes. The sign and goes from negative positive charity function is increasing after this point, and then it again reaches a plateau and it says almost constant. So that's why be there were two is almost zero again

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