Find $\frac { d y } { d x } \text { if } y = \ln \left( \frac { 5 x + 7 } { x ^ { 2 } - 4 } \right) ^ { 1 / 8 }$

question 41

Multiple Choice

Find $\frac { d y } { d x } \text { if } y = \ln \left( \frac { 5 x + 7 } { x ^ { 2 } - 4 } \right) ^ { 1 / 8 }$ .

• A) \(\frac { 5 x ^ { 2 } + 14 x + 5 } { 8 ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)
• B) \(- \frac { 5 x ^ { 2 } + 7 x + 20 } { ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)
• C) \(\frac { 5 x ^ { 2 } + 7 x + 20 } { 8 ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)
• D) \(\frac { 5 x ^ { 2 } + 14 x + 20 } { ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)
• E) \(- \frac { 5 x ^ { 2 } + 14 x + 20 } { 8 ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)

---

Definitions:

Columns

Vertical divisions in a table or spreadsheet, categorizing information by field.

Two-dimensional Array

A matrix-like structure that allows for storage and organization of data in rows and columns, facilitating operations on multi-dimensional data.

Function Prototype

A declaration of a function that specifies the function's name, return type, and parameters, used to inform the compiler about the function's existence before its actual definition.