Differentiate the Function $$f ( t ) = \frac { 2 + \ln t } { 5 - \ln t }$$

question 48

Multiple Choice

Differentiate the function. Select the correct answer.
$$f ( t ) = \frac { 2 + \ln t } { 5 - \ln t }$$

• A) \(f ^ { t } ( t ) = \frac { 7 } { t ( 1 - \ln t ) ^ { 2 } }\)
• B) \(f ^ { t } ( t ) = \frac { 7 } { t ( 5 - \ln t ) ^ { 2 } }\)
• C) \(f ^ { t } ( t ) = \frac { - 7 } { 5 t ( 2 - \ln t ) ^ { 3 } }\)
• D) \(f ^ { t } ( t ) = \frac { - 3 } { t ( 5 - \ln t ) ^ { 2 } }\)
• E) \(f ^ { t } ( t ) = \frac { 3 + 2 \ln t } { t ( 2 - \ln t ) ^ { 2 } }\)

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Definitions:

Acetyl Group

A 2-carbon group derived from acetic acid (acetate).

FADH₂

A reduced form of flavin adenine dinucleotide, a redox-active coenzyme involved in cellular respiration.

Aerobic Respiration

A metabolic process that uses oxygen to convert glucose or other organic substrates into energy, carbon dioxide, and water.

Electron Transport Chain

A series of protein complexes located in the inner mitochondrial membrane that facilitate electron transfer and ATP production.