Download the App!

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

Question

Answered step-by-step

(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". $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Clarissa Noh

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

00:29

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd College

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.

02:09

(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…

he It's clears the when you read here. So you have up of X is equal to X square minus one over X square plus one. We're gonna use a quotient role. To find our derivative, we get X square plus one D over deep rex of X square minus one minus X square minus one D over DX of X square plus one all over X square plus one square has becomes equal to X square plus one arms to X minus X square minus one times two x over X square plus one square. This becomes equal to four X over X squared, plus one square. Now we're gonna apply the same rule to find the second derivative when we get X Square plus one square D over D X for X minus for X times D over DX for X square plus one square all over X square plus one square and you score that again and then this simplifies into four minus 12 X square over X square plus one cubed. Here you apply the chain rule. Now we're going to draw some graphs for part B. We're going to start with R F of X so we'll draw down in black, an uncle like this, and our red is gonna be our derivative first derivative, and then our second derivative is gonna be in green.

View More Answers From This Book

Find Another Textbook