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
Hello, Please answer the following attached Calculus question correctly, and show all your work completely. Please make sure to write neatly and also box your answer. Thank you.
![**Logarithmic Differentiation Example**
Use logarithmic differentiation to find \(\frac{dy}{dx}\).
Given:
\[ y = (3x^4 - 2)^{\tan x} \]
**Explanation:**
In this problem, we are tasked with finding the derivative \(\frac{dy}{dx}\) of the function \(y = (3x^4 - 2)^{\tan x}\) using logarithmic differentiation. This technique is particularly useful when a variable exponent is involved, as it simplifies the differentiation process by utilizing logarithm properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d46332a-4771-46b4-8cc3-bfaffe8066c3%2Fb41c99af-178a-40cf-9697-2ac3f36f264a%2Ft7zmn69_processed.png&w=3840&q=75)
Transcribed Image Text:**Logarithmic Differentiation Example**
Use logarithmic differentiation to find \(\frac{dy}{dx}\).
Given:
\[ y = (3x^4 - 2)^{\tan x} \]
**Explanation:**
In this problem, we are tasked with finding the derivative \(\frac{dy}{dx}\) of the function \(y = (3x^4 - 2)^{\tan x}\) using logarithmic differentiation. This technique is particularly useful when a variable exponent is involved, as it simplifies the differentiation process by utilizing logarithm properties.
Expert Solution
Step 1
Here, the given function is:
Taking natural logerithm on both sides:
Step by step
Solved in 2 steps
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