If F(x) = $\frac { 1 } { x ^ { 3 } + x ^ { 2 } }$

question 54

Multiple Choice

If f(x) = $\frac { 1 } { x ^ { 3 } + x ^ { 2 } }$ , find $f ^ { \prime }$ (x) .

• A) \(\frac { 1 } { \left( x ^ { 3 } + x ^ { 2 } \right) ^ { 2 } }\)
• B) \(\frac { x ^ { 3 } + x ^ { 2 } } { \left( x ^ { 3 } + x ^ { 2 } \right) ^ { 2 } }\)
• C) \(\frac { - 3 x ^ { 2 } - 2 x } { \left( x ^ { 3 } + x ^ { 2 } \right) ^ { 2 } }\)
• D) - \(\frac { 2 x + 1 } { x ^ { 2 } ( x + 1 ) ^ { 2 } }\)

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Definitions:

Action Potentials

Rapid and temporary electrical impulses that travel across the membrane of nerve cells, facilitating neuronal communication.

Synapse

The junction between two neurons or between a neuron and muscle fiber, where electrical or chemical signals are transmitted.

All-or-none Law

A principle stating that the strength of a response of a nerve or muscle fiber is not dependent on the strength of the stimulus. If a stimulus is above a certain threshold, a nerve or muscle fiber will fire.

Physiological Explanation

Physiological explanation involves interpreting behaviors, functions, or responses in terms of the biological processes and structures underlying them.