Find $\frac { d y } { d x }$ If $y = \ln \left( x ^ { 9 } ( x + 5 ) ^ { \frac { 1 } { 2 } } \right)$

question 43

Multiple Choice

Find $\frac { d y } { d x }$ if $y = \ln \left( x ^ { 9 } ( x + 5 ) ^ { \frac { 1 } { 2 } } \right)$

• A) \(\frac { 9 ( 2 x + 5 ) } { 2 x ( x + 5 ) }\)
• B) \(\frac { 19 x + 90 } { 2 x ( x + 5 ) }\)
• C) \(\frac { 9 ( 2 x + 10 ) } { x ( x + 5 ) }\)
• D) \(\frac { 19 x + 45 } { x ( x + 5 ) }\)
• E) \(\frac { 19 x + 18 } { x ( x + 5 ) }\)

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Definitions:

Earnings Per Share

A measure of a company's profitability that is calculated by dividing its net earnings available to common shareholders by the average outstanding shares.

Common Stock

Represents equity ownership in a corporation, providing voting rights and entitling the holder to a share of the company's success through dividends and/or capital appreciation.

Fixed Asset Turnover

A financial ratio that measures a company's effectiveness in generating sales from its fixed assets.

Net Income

The amount of a company’s profit after all expenses, taxes, and costs have been subtracted from total revenue.