BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen.

y = x x , ( 1 , 0 )

To determine

To find: The equation of the tangent line to the curve and to sketch the given curve and the tangent line at the given point.

Explanation

Given:

The equation of the curve is y=xx and the point is (1,0).

Derivative rules:

(1) Power rule: ddx(xn)=nxn1

(2) Difference rule:ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

where, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

The derivative of y is dydx , which is obtained as follows.

dydx=ddx(y) =ddx(xx) =ddx(xx12) 

Apply the difference rule (2),

dydx=ddx(x)ddx(x12)  

Simplify the expression using the power rule (1),

dydx=(1x11)(12x121)  =(1x0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.1 P-53ESect-3.1 P-55ESect-3.1 P-56ESect-3.1 P-57ESect-3.1 P-58ESect-3.1 P-59ESect-3.1 P-60ESect-3.1 P-61ESect-3.1 P-62ESect-3.1 P-63ESect-3.1 P-64ESect-3.1 P-65ESect-3.1 P-66ESect-3.1 P-67ESect-3.1 P-68ESect-3.1 P-69ESect-3.1 P-70ESect-3.1 P-71ESect-3.1 P-72ESect-3.1 P-73ESect-3.1 P-74ESect-3.1 P-75ESect-3.1 P-76ESect-3.1 P-77ESect-3.1 P-78ESect-3.1 P-79ESect-3.1 P-80ESect-3.1 P-81ESect-3.1 P-82ESect-3.1 P-83ESect-3.1 P-84ESect-3.1 P-85ESect-3.1 P-86ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.2 P-37ESect-3.2 P-38ESect-3.2 P-39ESect-3.2 P-40ESect-3.2 P-41ESect-3.2 P-42ESect-3.2 P-43ESect-3.2 P-44ESect-3.2 P-45ESect-3.2 P-46ESect-3.2 P-47ESect-3.2 P-48ESect-3.2 P-49ESect-3.2 P-50ESect-3.2 P-51ESect-3.2 P-52ESect-3.2 P-53ESect-3.2 P-54ESect-3.2 P-55ESect-3.2 P-56ESect-3.2 P-57ESect-3.2 P-58ESect-3.2 P-59ESect-3.2 P-60ESect-3.2 P-61ESect-3.2 P-62ESect-3.2 P-63ESect-3.2 P-64ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 P-46ESect-3.3 P-47ESect-3.3 P-48ESect-3.3 P-49ESect-3.3 P-50ESect-3.3 P-51ESect-3.3 P-52ESect-3.3 P-53ESect-3.3 P-54ESect-3.3 P-55ESect-3.3 P-56ESect-3.3 P-57ESect-3.3 P-58ESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.4 P-43ESect-3.4 P-44ESect-3.4 P-45ESect-3.4 P-46ESect-3.4 P-47ESect-3.4 P-48ESect-3.4 P-49ESect-3.4 P-50ESect-3.4 P-51ESect-3.4 P-52ESect-3.4 P-53ESect-3.4 P-54ESect-3.4 P-55ESect-3.4 P-56ESect-3.4 P-57ESect-3.4 P-58ESect-3.4 P-59ESect-3.4 P-60ESect-3.4 P-61ESect-3.4 P-62ESect-3.4 P-63ESect-3.4 P-64ESect-3.4 P-65ESect-3.4 P-66ESect-3.4 P-67ESect-3.4 P-68ESect-3.4 P-69ESect-3.4 P-70ESect-3.4 P-71ESect-3.4 P-72ESect-3.4 P-73ESect-3.4 P-74ESect-3.4 P-75ESect-3.4 P-76ESect-3.4 P-77ESect-3.4 P-78ESect-3.4 P-79ESect-3.4 P-80ESect-3.4 P-81ESect-3.4 P-82ESect-3.4 P-83ESect-3.4 P-84ESect-3.4 P-85ESect-3.4 P-86ESect-3.4 P-87ESect-3.4 P-88ESect-3.4 P-89ESect-3.4 P-90ESect-3.4 P-93ESect-3.4 P-94ESect-3.4 P-95ESect-3.4 P-96ESect-3.4 P-97ESect-3.4 P-98ESect-3.4 P-99ESect-3.4 P-100ESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.5 P-40ESect-3.5 P-43ESect-3.5 P-44ESect-3.5 P-45ESect-3.5 P-46ESect-3.5 P-47ESect-3.5 P-48ESect-3.5 P-49ESect-3.5 P-50ESect-3.5 P-51ESect-3.5 P-52ESect-3.5 P-53ESect-3.5 P-54ESect-3.5 P-55ESect-3.5 P-56ESect-3.5 P-57ESect-3.5 P-58ESect-3.5 P-59ESect-3.5 P-60ESect-3.5 P-61ESect-3.5 P-62ESect-3.5 P-63ESect-3.5 P-64ESect-3.5 P-65ESect-3.5 P-66ESect-3.5 P-67ESect-3.5 P-68ESect-3.5 P-69ESect-3.5 P-70ESect-3.5 P-71ESect-3.5 P-73ESect-3.5 P-74ESect-3.5 P-75ESect-3.5 P-76ESect-3.5 P-77ESect-3.5 P-78ESect-3.5 P-79ESect-3.5 P-80ESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25ESect-3.6 P-26ESect-3.6 P-27ESect-3.6 P-28ESect-3.6 P-29ESect-3.6 P-30ESect-3.6 P-31ESect-3.6 P-32ESect-3.6 P-33ESect-3.6 P-34ESect-3.6 P-35ESect-3.6 P-36ESect-3.6 P-37ESect-3.6 P-38ESect-3.6 P-39ESect-3.6 P-40ESect-3.6 P-41ESect-3.6 P-42ESect-3.6 P-43ESect-3.6 P-44ESect-3.6 P-45ESect-3.6 P-46ESect-3.6 P-47ESect-3.6 P-48ESect-3.6 P-49ESect-3.6 P-50ESect-3.6 P-51ESect-3.6 P-52ESect-3.6 P-53ESect-3.6 P-54ESect-3.6 P-55ESect-3.6 P-56ESect-3.7 P-1ESect-3.7 P-2ESect-3.7 P-3ESect-3.7 P-4ESect-3.7 P-5ESect-3.7 P-6ESect-3.7 P-7ESect-3.7 P-8ESect-3.7 P-9ESect-3.7 P-10ESect-3.7 P-11ESect-3.7 P-12ESect-3.7 P-13ESect-3.7 P-14ESect-3.7 P-15ESect-3.7 P-16ESect-3.7 P-17ESect-3.7 P-18ESect-3.7 P-19ESect-3.7 P-20ESect-3.7 P-21ESect-3.7 P-22ESect-3.7 P-23ESect-3.7 P-24ESect-3.7 P-25ESect-3.7 P-26ESect-3.7 P-28ESect-3.7 P-29ESect-3.7 P-30ESect-3.7 P-31ESect-3.7 P-32ESect-3.7 P-33ESect-3.7 P-34ESect-3.7 P-35ESect-3.7 P-36ESect-3.7 P-37ESect-3.7 P-38ESect-3.7 P-39ESect-3.8 P-1ESect-3.8 P-2ESect-3.8 P-3ESect-3.8 P-4ESect-3.8 P-5ESect-3.8 P-6ESect-3.8 P-7ESect-3.8 P-8ESect-3.8 P-9ESect-3.8 P-10ESect-3.8 P-11ESect-3.8 P-12ESect-3.8 P-13ESect-3.8 P-14ESect-3.8 P-15ESect-3.8 P-16ESect-3.8 P-17ESect-3.8 P-18ESect-3.8 P-19ESect-3.8 P-20ESect-3.8 P-21ESect-3.8 P-22ESect-3.9 P-1ESect-3.9 P-2ESect-3.9 P-3ESect-3.9 P-4ESect-3.9 P-5ESect-3.9 P-6ESect-3.9 P-7ESect-3.9 P-8ESect-3.9 P-9ESect-3.9 P-10ESect-3.9 P-11ESect-3.9 P-12ESect-3.9 P-13ESect-3.9 P-14ESect-3.9 P-15ESect-3.9 P-16ESect-3.9 P-17ESect-3.9 P-18ESect-3.9 P-19ESect-3.9 P-20ESect-3.9 P-21ESect-3.9 P-22ESect-3.9 P-23ESect-3.9 P-24ESect-3.9 P-25ESect-3.9 P-26ESect-3.9 P-27ESect-3.9 P-28ESect-3.9 P-29ESect-3.9 P-30ESect-3.9 P-31ESect-3.9 P-32ESect-3.9 P-33ESect-3.9 P-34ESect-3.9 P-35ESect-3.9 P-36ESect-3.9 P-37ESect-3.9 P-38ESect-3.9 P-39ESect-3.9 P-40ESect-3.9 P-41ESect-3.9 P-42ESect-3.9 P-43ESect-3.9 P-44ESect-3.9 P-45ESect-3.9 P-46ESect-3.9 P-47ESect-3.9 P-48ESect-3.9 P-49ESect-3.9 P-50ESect-3.10 P-1ESect-3.10 P-2ESect-3.10 P-3ESect-3.10 P-4ESect-3.10 P-5ESect-3.10 P-6ESect-3.10 P-7ESect-3.10 P-8ESect-3.10 P-9ESect-3.10 P-10ESect-3.10 P-11ESect-3.10 P-12ESect-3.10 P-13ESect-3.10 P-14ESect-3.10 P-15ESect-3.10 P-16ESect-3.10 P-17ESect-3.10 P-18ESect-3.10 P-19ESect-3.10 P-20ESect-3.10 P-21ESect-3.10 P-22ESect-3.10 P-23ESect-3.10 P-24ESect-3.10 P-25ESect-3.10 P-26ESect-3.10 P-27ESect-3.10 P-28ESect-3.10 P-29ESect-3.10 P-30ESect-3.10 P-31ESect-3.10 P-32ESect-3.10 P-33ESect-3.10 P-34ESect-3.10 P-35ESect-3.10 P-36ESect-3.10 P-37ESect-3.10 P-38ESect-3.10 P-39ESect-3.10 P-40ESect-3.10 P-41ESect-3.10 P-42ESect-3.10 P-43ESect-3.10 P-44ESect-3.11 P-1ESect-3.11 P-2ESect-3.11 P-3ESect-3.11 P-4ESect-3.11 P-5ESect-3.11 P-6ESect-3.11 P-7ESect-3.11 P-8ESect-3.11 P-9ESect-3.11 P-10ESect-3.11 P-11ESect-3.11 P-12ESect-3.11 P-13ESect-3.11 P-14ESect-3.11 P-15ESect-3.11 P-16ESect-3.11 P-17ESect-3.11 P-18ESect-3.11 P-19ESect-3.11 P-20ESect-3.11 P-21ESect-3.11 P-22ESect-3.11 P-23ESect-3.11 P-24ESect-3.11 P-25ESect-3.11 P-26ESect-3.11 P-27ESect-3.11 P-28ESect-3.11 P-29ESect-3.11 P-30ESect-3.11 P-31ESect-3.11 P-32ESect-3.11 P-33ESect-3.11 P-34ESect-3.11 P-35ESect-3.11 P-36ESect-3.11 P-37ESect-3.11 P-38ESect-3.11 P-39ESect-3.11 P-40ESect-3.11 P-41ESect-3.11 P-42ESect-3.11 P-43ESect-3.11 P-44ESect-3.11 P-45ESect-3.11 P-46ESect-3.11 P-47ESect-3.11 P-48ESect-3.11 P-49ESect-3.11 P-50ESect-3.11 P-51ESect-3.11 P-52ESect-3.11 P-53ESect-3.11 P-54ESect-3.11 P-55ESect-3.11 P-56ESect-3.11 P-57ESect-3.11 P-58ECh-3 P-1RCCCh-3 P-2RCCCh-3 P-3RCCCh-3 P-4RCCCh-3 P-5RCCCh-3 P-6RCCCh-3 P-7RCCCh-3 P-1RQCh-3 P-2RQCh-3 P-3RQCh-3 P-4RQCh-3 P-5RQCh-3 P-6RQCh-3 P-7RQCh-3 P-8RQCh-3 P-9RQCh-3 P-10RQCh-3 P-11RQCh-3 P-12RQCh-3 P-13RQCh-3 P-14RQCh-3 P-15RQCh-3 P-1RECh-3 P-2RECh-3 P-3RECh-3 P-4RECh-3 P-5RECh-3 P-6RECh-3 P-7RECh-3 P-8RECh-3 P-9RECh-3 P-10RECh-3 P-11RECh-3 P-12RECh-3 P-13RECh-3 P-14RECh-3 P-15RECh-3 P-16RECh-3 P-17RECh-3 P-18RECh-3 P-19RECh-3 P-20RECh-3 P-21RECh-3 P-22RECh-3 P-23RECh-3 P-24RECh-3 P-25RECh-3 P-26RECh-3 P-27RECh-3 P-28RECh-3 P-29RECh-3 P-30RECh-3 P-31RECh-3 P-32RECh-3 P-33RECh-3 P-34RECh-3 P-35RECh-3 P-36RECh-3 P-37RECh-3 P-38RECh-3 P-39RECh-3 P-40RECh-3 P-41RECh-3 P-42RECh-3 P-43RECh-3 P-44RECh-3 P-45RECh-3 P-46RECh-3 P-47RECh-3 P-48RECh-3 P-49RECh-3 P-50RECh-3 P-51RECh-3 P-52RECh-3 P-53RECh-3 P-54RECh-3 P-55RECh-3 P-56RECh-3 P-57RECh-3 P-58RECh-3 P-59RECh-3 P-60RECh-3 P-61RECh-3 P-62RECh-3 P-63RECh-3 P-64RECh-3 P-65RECh-3 P-66RECh-3 P-67RECh-3 P-68RECh-3 P-69RECh-3 P-70RECh-3 P-71RECh-3 P-72RECh-3 P-73RECh-3 P-74RECh-3 P-75RECh-3 P-76RECh-3 P-77RECh-3 P-78RECh-3 P-79RECh-3 P-80RECh-3 P-81RECh-3 P-82RECh-3 P-83RECh-3 P-84RECh-3 P-85RECh-3 P-86RECh-3 P-87RECh-3 P-88RECh-3 P-89RECh-3 P-90RECh-3 P-91RECh-3 P-92RECh-3 P-93RECh-3 P-94RECh-3 P-95RECh-3 P-96RECh-3 P-97RECh-3 P-98RECh-3 P-99RECh-3 P-100RECh-3 P-101RECh-3 P-102RECh-3 P-103RECh-3 P-104RECh-3 P-105RECh-3 P-106RECh-3 P-107RECh-3 P-108RECh-3 P-109RECh-3 P-110RECh-3 P-111RECh-3 P-112RECh-3 P-1PCh-3 P-2PCh-3 P-3PCh-3 P-4PCh-3 P-5PCh-3 P-6PCh-3 P-7PCh-3 P-8PCh-3 P-9PCh-3 P-10PCh-3 P-11PCh-3 P-12PCh-3 P-13PCh-3 P-14PCh-3 P-15PCh-3 P-16PCh-3 P-17PCh-3 P-18PCh-3 P-19PCh-3 P-20PCh-3 P-21PCh-3 P-22PCh-3 P-23PCh-3 P-24PCh-3 P-25PCh-3 P-27PCh-3 P-28PCh-3 P-29PCh-3 P-30PCh-3 P-31PCh-3 P-32PCh-3 P-33PCh-3 P-34PCh-3 P-35P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Determine the infinite limit. limxcotx

Single Variable Calculus: Early Transcendentals, Volume I

Solving Equations Find all real solutions of the equation. 63. 4x3 25x = 0

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the definite integral. 12xx1dx

Calculus (MindTap Course List)

In Exercises 23-36, find the domain of the function. 24. f(x) = 7 x2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

The equation of the tangent plane to for is:

Study Guide for Stewart's Multivariable Calculus, 8th

Evaluate ∫16t3 ln t dt. 4t4 + C 4t3 ln t − 16t3 + C 4t4 − t3 ln t + C 4t4 ln t − t4 + C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th