Find the Derivative of Y with Respect to the Appropriate $$y = \left( \theta ^ { 2 } + 4 \theta \right) \tanh ^ { - 1 } ( \theta + 3 )$$

question 133

Multiple Choice

Find the derivative of y with respect to the appropriate variable.
- $$y = \left( \theta ^ { 2 } + 4 \theta \right) \tanh ^ { - 1 } ( \theta + 3 )$$

• A) \(( 2 \theta + 4 ) \tanh ^ { - 1 } ( \theta + 3 ) - \frac { \theta } { \theta + 2 }\)
• B) \(( 2 \theta + 4 ) - \frac { 1 } { \theta + 8 }\)
• C) \(( 2 \theta + 4 ) \tanh ^ { - 1 } ( \theta + 3 ) - \frac { \theta ^ { 2 } + 4 \theta } { 1 + ( \theta + 3 ) ^ { 2 } }\)
• D) \(- \frac { \theta } { \theta + 2 }\)

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Definitions:

Cost of Goods Manufactured

The total production cost incurred by a company to manufacture products in a specific period, including costs of materials, labor, and overhead.

Job-Order Costing

Job-order costing is an accounting method that tracks costs individually by job or order, suitable for customized orders or distinct projects.

Direct Labour

Direct labour refers to the work of employees who are directly involved in the production of goods or the delivery of services, opposite to indirect labor.

Overhead

The general operating costs not directly tied to production, including administrative and facility expenses.