/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 42. Find the derivatives of each of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q 42. (page 222)

Find the derivatives of each of functions in Exercises 17鈥�44. In some cases it may be convenient to do some preliminary algebra.

fx=Inxx

Short Answer

Expert verified

The required answer islnx+1.

Step by step solution

01

Step 1. Given information.

The given function is:

fx=Inxx

02

Step 2. Find the derivative of the given function.

fx=Inxxf'x=ddxInxx=ddxxlnx=lnx路dxdx+xddxlnx=lnx+x路1x=lnx+1

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating

a)f(x)=(3x+1)4b)f(x)=(1x+1x2)2c)f(x)=(x+1)2xd)f(x)=(x+1)2x

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=7x2+8x11-18;f(0)=-2

For each function f that follows find all the x-values in the domain of f for which f'(x)=0and all the values for which f'(x)does not exist in later section we will call these values the critical points of f

localid="1648604345877" a)f(x)=x3-2xb)f(x)=x-xc)鈥�f(x)=11+xd)f(x)=x2(x-1)(x-2)2

Prove that if f is a quadratic polynomial function f(x)=ax2+bx+cthen the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows

a=f"(0)2;b=f'(0);c=f(0)

Use the definition of the derivative to find f' for each function f in Exercises 39-54

f(x)=-x3-x+1
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.