Find the Derivative of the Given Function $c ( x ) = 3 x \sqrt { x ^ { 9 } + 7 }$

question 52

Multiple Choice

Find the derivative of the given function. Simplify and express the answer using positive exponents only. $c ( x ) = 3 x \sqrt { x ^ { 9 } + 7 }$

• A) \(\frac { 3 \left( 11 x ^ { 9 } - 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }\)
• B) \(\frac { 3 \left( 9 x ^ { 9 } - 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }\)
• C) \(\frac { 3 \left( 9 x ^ { 9 } - 14 \right) } { \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }\)
• D) \(\frac { 3 \left( 11 x ^ { 9 } + 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }\)
• E) \(\frac { 3 \left( 9 x ^ { 9 } + 14 \right) } { \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }\)

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Definitions:

Annual Dividend

The total dividend payment a company distributes to its shareholders annually.

Rate of Return

The appreciation or depreciation in value of an investment over an agreed period, conveyed as a percentage of the investment's starting value.

Dividend Increase

An action taken by a company's board of directors to raise the amount paid out to shareholders in dividends.

Required Return

The smallest anticipated return that an investor looks to obtain by putting money into a certain asset, factoring in the risk entailed.