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If g(z) = 6-2), then its derivative is given by:

If g(z) = 6-2), then its derivative is given by:

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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Question
The image shows four mathematical expressions, which appear to be different forms or steps in the differentiation process of a function involving natural logarithms and exponential expressions. Here are the expressions listed: 1. \( g'(x) = x^2 \cdot \ln 6 \cdot 6^{(x^2 - 2)} \) 2. \( g'(x) = (x^2 - 2) \cdot \ln 6 \cdot 6^{(x^2 - 3)} \) 3. \( g'(x) = \ln 6 \cdot 6^{(x^2 - 2)} \) 4. \( g'(x) = 2x \cdot \ln 6 \cdot 6^{(x^2 - 2)} \) These expressions likely relate to the differentiation process or manipulation of a function \( g(x) \) that involves powers and logarithms, particularly focusing on the natural logarithm of 6 and powers of the base 6. The expressions may indicate steps or errors in the differentiation or simplification process.
Transcribed Image Text:The image shows four mathematical expressions, which appear to be different forms or steps in the differentiation process of a function involving natural logarithms and exponential expressions. Here are the expressions listed: 1. \( g'(x) = x^2 \cdot \ln 6 \cdot 6^{(x^2 - 2)} \) 2. \( g'(x) = (x^2 - 2) \cdot \ln 6 \cdot 6^{(x^2 - 3)} \) 3. \( g'(x) = \ln 6 \cdot 6^{(x^2 - 2)} \) 4. \( g'(x) = 2x \cdot \ln 6 \cdot 6^{(x^2 - 2)} \) These expressions likely relate to the differentiation process or manipulation of a function \( g(x) \) that involves powers and logarithms, particularly focusing on the natural logarithm of 6 and powers of the base 6. The expressions may indicate steps or errors in the differentiation or simplification process.
If \( g(x) = 6^{(x^2 - 2)} \), then its derivative is given by:
Transcribed Image Text:If \( g(x) = 6^{(x^2 - 2)} \), then its derivative is given by:
Expert Solution
Step 1

Consider the following formula:

ddxax=lna·ax

Consider the following function:

gx=6x2-2

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