2. (13) The derivative of The derivative ofrequires the product rule and is given byFactor the derivative of f.g'(v)g(v) = (v7) (v+6)²g′(v) = (v − 7)ª(2(v + 6)) + (v + 6)²³ ( 4 (v — 7)³)

Given:Here we have given a function .To find:The derivative of the given function using product…

Answered: The derivative of requires the product…

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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2. (13) The derivative of

The derivative of
requires the product rule and is given by
Factor the derivative of f.
g'(v)
g(v) = (v7) (v+6)²
g′(v) = (v − 7)ª(2(v + 6)) + (v + 6)²³ ( 4 (v — 7)³)

Expert Solution

Step 1: Given:

Given:
Here we have given a function $g left parenthesis v right parenthesis equals left parenthesis v minus 7 right parenthesis to the power of 4 left parenthesis v plus 6 right parenthesis squared$ .

To find:
The derivative of the given function using product rule.

Product rule for derivative of a function:

Let us suppose a function $f space equals space u times v$ .

Then derivative of the given function will be :
$f apostrophe equals v left parenthesis u apostrophe right parenthesis plus u left parenthesis v apostrophe right parenthesis$