Homework Help is Here – Start Your Trial Now!
Math
Calculus
11. f(x) = 4x³ In(5x² +1)

11. f(x) = 4x³ In(5x² +1)

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
11.) find derivative
**Function Definition** In this image, the given function is defined as follows: \[ f(x) = 4x^3 \ln(5x^2 + 1) \] This mathematical function represents a combination of polynomial and logarithmic elements. Specifically, it is the product of a cubic polynomial \(4x^3\) and the natural logarithm function \(\ln(5x^2 + 1)\). In analyzing such functions, one might explore concepts like differentiation or integration, examining how the polynomial interacts with the logarithmic component over different values of \(x\).
Transcribed Image Text:**Function Definition** In this image, the given function is defined as follows: \[ f(x) = 4x^3 \ln(5x^2 + 1) \] This mathematical function represents a combination of polynomial and logarithmic elements. Specifically, it is the product of a cubic polynomial \(4x^3\) and the natural logarithm function \(\ln(5x^2 + 1)\). In analyzing such functions, one might explore concepts like differentiation or integration, examining how the polynomial interacts with the logarithmic component over different values of \(x\).
Expert Solution
Step 1

Topic-Derivative of a function

We are given,f(x)=4x3ln(5x2+1)we know thatddx(u.v)=uv'+vu'ddxln(f(x))=1f(x)f'(x)ddxxn=nxn-1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
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
SEE MORE TEXTBOOKS