Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(a) $f^{\prime}(x)=\frac{x e^{x}(2 x-3)}{\left(2 x^{2}+x+1\right)^{2}}$(b) See explanation for result

00:36

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Idaho State 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.

04:20

(a) If $ f(x) = e^x/ (2x^2…

02:21

(a) If $ f(x) = (x^2 - 1) …

03:45

$\begin{array}{l}{\text { …

06:13

(a) If $f ( x ) = \left( x…

02:38

02:15

06:50

(a) If $f(x)=x+1 / x,$ fin…

07:55

(a) If f(x) = x2 ? 1/x…

it's clear. So when you raid here, So we're gonna take the derivative and we're gonna apply our quotient role. And we got two x square plus x plus one times e to the X minus. Each of the ex comes for X plus one all over X square, two X square plus X plus one square. This becomes equal to sex each X Times two X minus three All over to X square plus X plus one square For a second part, we're gonna draw a graph. I'll draw our original in black so look like this and then our derivative and red

View More Answers From This Book

Find Another Textbook

01:41

Find the value of Y-y = [ ? 18

06:03

Consider triangle ABC like the one below. Suppose that a=33,b=27, and € = 14…

05:37

sinx dxe VcosxTwti (U) tan- 10_sec rdx

08:32

Ata local bar in small Midwestern town beer and wine are the only two alcoho…

7(y complele)Find polynomial function af lowest degree with rational coe…

01:28

Find the exact length of the unknown side of the triangle shown t0 the right…

01:38

Assume Iriangle ABC has standard labeling: (a) Determine whelher SAA,ASA, SS…

03:50

Find the area of the triangle ABC_a = 346 cm b =231 cm c=422 cmWhat …

04:17

Inventory: ABC Auto sells 400 new automobiles a year, It costs 5100 store on…

01:16

If ene centimeter on a map represents 280 kilometers what is the scale ratio…