(8) Please show work as necessary. Differentiate.$ f(x) = x^3 \ln 7x $\[ f'(x) = \text{[ ]} \]In this image, we are given a function $ f(x) = x^3 \ln 7x $ and asked to find its derivative $ f'(x) $. The derivative should be calculated using the product rule and chain rule for differentiation. The expression $ \ln $ denotes the natural logarithm. The answer is to be filled in the provided box.

Answered: Differentiate. f(x)= x³ In 7x 3 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...

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Question

(8) Please show work as necessary.

Differentiate.

$ f(x) = x^3 \ln 7x $

\[ f'(x) = \text{[ ]} \]

In this image, we are given a function $ f(x) = x^3 \ln 7x $ and asked to find its derivative $ f'(x) $. The derivative should be calculated using the product rule and chain rule for differentiation. The expression $ \ln $ denotes the natural logarithm. The answer is to be filled in the provided box.

Expert Solution

Step 1: Product Formula for differentiation

Product Formula for differentiation is given as follows

$fraction numerator d blank over denominator d x end fraction left parenthesis space u. v space right parenthesis space equals space u fraction numerator d v over denominator d x end fraction space plus space v fraction numerator d u over denominator d x end fraction$