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(a) If $ f(x) = (x^2 - 1) e^x, $ find $ f' (x) $ and $ f" (x). $(b) Check to see that your answers to part (a) are reasonable by comparing the graphs of $ f, f', $ and $ f". $

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00:39

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

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.

02:38

$\begin{array}{l}{\text { …

03:45

02:09

(a) If $ f(x) = e^x/ (2x^2…

04:20

06:13

(a) If $f ( x ) = \left( x…

02:15

06:50

(a) If $f(x)=x+1 / x,$ fin…

02:39

03:49

(a) If $ f(x) = (x^3 - x)e…

07:55

(a) If f(x) = x2 ? 1/x…

Yes. Close. So when you married here, so we have ever backs is equal to x square minus one times e to the X. We're gonna find our derivative by using the product rule yet to ex homes, Eat the X goes eat two x times X square minus one. This is equal to eat the X x square plus to minus one. To get our second derivative, we're gonna use the product rule again. Get E to the X from specs square Those two X minus one must two X plus two e to the X, which is equal to eat The axe. Times Square was for X plus one. Next, we're going to draw our graphs wound. Don't look like this.

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