4 Find the derivative of f(x) = x¹ log7(x + 4.5). f'(x) =

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Find the derivative of f( x ) = x² log7(x + 4.5).
f'(x) =
Transcribed Image Text:Find the derivative of f( x ) = x² log7(x + 4.5). f'(x) =
Expert Solution
Step 1

Given that

f(x)=x4log7(x+4.5)

Differentiating with respect to x

f'(x)=ddx(x4log7(x+4.5))=ddx(x4)*log7(x+4.5)+x4ddx(log7(x+4.5))=4x3log7(x+4.5)+x4*1ln7x+4.5=4x3log7(x+4.5)+x4ln(7)(x+4.5)=x4+4x3lnx+4.5x+4.5ln7x+4.5

[Derivative Formula

Product rule f·g'=f'·g+f·g'ddx(loga(x+b))=1ln(a)(x+b)ddx(xn)=nxn-1]

 

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning