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4. Find a formula for the nth derivative f(n)(x) of f(x) = ln(1+3x). Show some work computing the first few derivatives and then explain your reasoning for extrapolating to the general formula. You may use the factorial notation n! = n(n-1)(n-2) (2) (1) (for example 6!6-5-4-3-2-1 =720).

4. Find a formula for the nth derivative f(n)(x) of f(x) = ln(1+3x). Show some work computing the first few derivatives and then explain your reasoning for extrapolating to the general formula. You may use the factorial notation n! = n(n-1)(n-2) (2) (1) (for example 6!6-5-4-3-2-1 =720).

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...
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**Problem 4**: Find a formula for the \( n^{th} \) derivative \( f^{(n)}(x) \) of \( f(x) = \ln(1+3x) \). Show some work computing the first few derivatives and then explain your reasoning for extrapolating to the general formula. You may use the factorial notation \( n! = n(n-1)(n-2)\cdots (2)(1) \) (for example \( 6! = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 720 \)).
Transcribed Image Text:**Problem 4**: Find a formula for the \( n^{th} \) derivative \( f^{(n)}(x) \) of \( f(x) = \ln(1+3x) \). Show some work computing the first few derivatives and then explain your reasoning for extrapolating to the general formula. You may use the factorial notation \( n! = n(n-1)(n-2)\cdots (2)(1) \) (for example \( 6! = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 720 \)).
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