Find the Derivative of Y with Respect to the Appropriate $$y = \sinh ^ { - 1 } ( \cos x )$$

question 51

Multiple Choice

Find the derivative of y with respect to the appropriate variable.
- $$y = \sinh ^ { - 1 } ( \cos x )$$

• A) \(- \sin x\)
• B) \(\frac { 1 } { \sqrt { 1 + \cos ^ { 2 } x } }\)
• C) \(\frac { - \sin x } { \sqrt { 1 + x ^ { 2 } } }\)
• D) \(\frac { - \sin x } { \sqrt { 1 + \cos ^ { 2 } x } }\)

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Definitions:

HS

A logical argument pattern of hypothetical syllogism, involving two conditional statements leading to a conclusion.

MP

Stands for "Member of Parliament," but in a logical context, it refers to a deductive pattern of reasoning where a specific conclusion is inferred from a general rule and a specific case.

Conj

An abbreviation for "Conjunction," a logical operator that connects two conditions or propositions where both must be true.

Inference Forms

Patterns of reasoning where specific statements lead logically to a conclusion.