Find the Derivative Of $f ( x ) = ( x - \sqrt { x } ) ( x + \sqrt { x } )$

question 239

Multiple Choice

Find the derivative of $f ( x ) = ( x - \sqrt { x } ) ( x + \sqrt { x } )$ .

• A) \(\left( 1 - \frac { 1 } { \sqrt { x } } \right) \left( 1 + \frac { 1 } { \sqrt { x } } \right)\)
• B) \(2 x - 1\)
• C) \(\left( 1 - \frac { 1 } { 2 \sqrt { x } } \right) \left( 1 + \frac { 1 } { 2 \sqrt { x } } \right)\)
• D) \(2 x + 1\)
• E) \(\left( 1 - \frac { 1 } { 2 \sqrt { x } } \right) \left( 1 + \frac { 1 } { \sqrt { x } } \right)\)
• F) \(x - 1\)
• G) \(\left( 1 - \frac { 1 } { \sqrt { x } } \right) \left( 1 + \frac { 1 } { 2 \sqrt { x } } \right)\)
• H)None of these

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Definitions:

Grignard Reaction

A chemical reaction in which an alkyl, vinyl, or aryl-magnesium halide (Grignard reagent) adds to a carbonyl group in an aldehyde or ketone.

Epoxide

A cyclic ether with a three-atom ring, consisting of an oxygen atom and two carbon atoms.

Aldehyde

Organic compounds characterized by the presence of a carbonyl group bonded to at least one hydrogen atom.

Ketone

An organic compound characterized by a carbonyl group bonded to two other carbon atoms; important in organic chemistry and biology.