Simplify the Expression Representing the Derivative of a Function $$f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$$

question 113

Multiple Choice

Simplify the expression representing the derivative of a function.
- $$f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$$

• A) \(24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } - 36 x ^ { 2 } - 36 x + 18\)
• B) \(24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x + 18\)
• C) \(24 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x - 18\)
• D) \(24 x ^ { 5 } - 18 x ^ { 4 } - 18 x ^ { 2 } - 30 x + 18\)

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Definitions:

Resting Potential

The difference in voltage across the neuronal membrane when the neuron is not actively sending a signal, typically around -70mV.

Membrane Potential

The electrical potential difference across a cell's plasma membrane, crucial for the transmission of nerve impulses and muscle contraction.

Millivolts

A unit of electric potential equal to one thousandth of a volt, commonly used in various fields such as physics and electrophysiology to measure small voltage differences.

All-Or-None

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 with full strength.