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) \(- \frac { 5 x ^ { 2 } + 14 x + 20 } { 8 ( 5 x + 7 ) \left( x ^ { 2 } - 4 \right) }\)

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Definitions:

Annual Dividend

The total dividend payment a company distributes to its shareholders in a fiscal year.

Cumulative Preferred Stock

Preferred stock where dividends accumulate if not paid in a given year and must be paid out before dividends can be distributed to common stockholders.

Par Value

The nominal or face value of a bond, share of stock, or coupon as stated by the issuer.

Dividends Received

Refers to the payments received by shareholders from a company's earnings, typically distributed periodically.