Use Logarithmic Differentiation to Find the Derivative of Y $$y = \frac { x \sqrt { x ^ { 5 } + 1 } } { ( x + 6 ) ^ { 2 / 3 } }$$

question 107

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \frac { x \sqrt { x ^ { 5 } + 1 } } { ( x + 6 ) ^ { 2 / 3 } }$$

• A) \(\ln x + \frac { 1 } { 2 } \ln \left( x ^ { 5 } + 1 \right) - \frac { 2 } { 3 } \ln ( x + 6 )\)
• B) \(\frac { x \sqrt { x ^ { 5 } + 1 } } { ( x + 6 ) ^ { 2 / 3 } } \left( \ln x + \frac { 1 } { 2 } \ln \left( x ^ { 5 } + 1 \right) - \frac { 2 } { 3 } \ln ( x + 6 ) \right)\)
• C) \(\frac { 1 } { x } + \frac { 5 x ^ { 4 } } { 2 x ^ { 5 } + 2 } - \frac { 2 } { 3 x + 18 }\)
• D) \(\frac { x \sqrt { x ^ { 5 } + 1 } } { ( x + 6 ) ^ { 2 / 3 } } \left( \frac { 1 } { x } + \frac { 5 x ^ { 4 } } { 2 x ^ { 5 } + 2 } - \frac { 2 } { 3 x + 18 } \right)\)

---

Definitions:

Definition By Negation

Defining a concept by describing what it is not, instead of detailing its characteristics.

Class Definition

In programming, the specification of a new type of object, including its attributes and behaviors, within the context of object-oriented languages.

Emoticons

Text-based symbols used to convey emotions or sentiments in digital communication, predating modern emojis.

Sentence 1

This appears to be a placeholder rather than a key term, and thus cannot be defined contextually.