Use Logarithmic Differentiation to Find the Derivative of Y $$y = \sqrt [ 3 ] { \frac { x ( x - 9 ) } { x ^ { 3 } + 5 } }$$

question 231

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \sqrt [ 3 ] { \frac { x ( x - 9 ) } { x ^ { 3 } + 5 } }$$

• A) \(\frac { 1 } { 3 } \sqrt [ 3 ] { \frac { x ( x - 9 ) } { x ^ { 3 } + 5 } } \left( \frac { 1 } { x } + \frac { 1 } { x - 9 } - \frac { 3 x ^ { 2 } } { x ^ { 3 } + 5 } \right)\)
• B) \(\frac { 1 } { 3 } \left( \ln x + \ln ( x - 9 ) - \ln \left( x ^ { 3 } + 5 \right) \right)\)
• C) \(\frac { 1 } { x } + \frac { 1 } { x - 9 } - \frac { 3 x ^ { 2 } } { x ^ { 3 } + 5 }\)
• D) \(3 \sqrt [ 3 ] { \frac { x ( x - 9 ) } { x ^ { 3 } + 5 } } \left( \frac { 1 } { x } + \frac { 1 } { x - 9 } - \frac { 3 x ^ { 2 } } { x ^ { 3 } + 5 } \right)\)

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Definitions:

Urinary

Relating to the system of organs responsible for the production, storage, and expulsion of urine.

Stratified Squamous

A type of epithelial tissue characterized by multiple layers of flat, closely packed cells, which provides protection against mechanical stress and abrasion.

Simple Cuboidal

Epithelial cells shaped like cubes or squares; these cells are found in glands and ducts and function in secretion or absorption.

Epithelium

a layer of cells forming the epidermis of the skin and the surface layer of mucous and serous membranes, playing roles in protection, secretion, and absorption.