Find the Derivative of Y with Respect to the Appropriate $$y = \left( \theta ^ { 2 } + 9 \theta \right) \tanh ^ { - 1 } ( \theta + 8 )$$

question 3

Multiple Choice

Find the derivative of y with respect to the appropriate variable.
- $$y = \left( \theta ^ { 2 } + 9 \theta \right) \tanh ^ { - 1 } ( \theta + 8 )$$

• A) \(- \frac { \theta } { \theta + 7 }\)
• B) \(( 2 \theta + 9 ) \tanh ^ { - 1 } ( \theta + 8 ) - \frac { \theta ^ { 2 } + 9 \theta } { 1 + ( \theta + 8 ) ^ { 2 } }\)
• C) \(( 2 \theta + 9 ) \tanh ^ { - 1 } ( \theta + 8 ) - \frac { \theta } { \theta + 7 }\)
• D) \(( 2 \theta + 9 ) - \frac { 1 } { \theta + 63 }\)

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Definitions:

Unconditioned Stimulus

A stimulus that automatically triggers a natural and unlearned response.

Neutral Stimulus

An initially meaningless stimulus that, when consistently paired with an unconditioned stimulus, can acquire the capacity to elicit a conditioned response.

Conditioned Response

A learned response to a previously neutral stimulus that has been repeatedly presented alongside an unconditioned stimulus.

CR

Conditioned Response; a learned response to a previously neutral stimulus that has been repeatedly associated with an unconditioned stimulus.