Find the Derivative of Y $$y = - 5 t ^ { 3 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right)$$

question 24

Multiple Choice

Find the derivative of y.
- $$y = - 5 t ^ { 3 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right)$$

• A) \(- 15 t ^ { 2 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right) + 10 \operatorname { sech } \left( \frac { 1 } { t ^ { 2 } } \right)\)
• B) \(- 15 t ^ { 2 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right) + 5 \operatorname { sech } ^ { 2 } \left( \frac { 1 } { t ^ { 2 } } \right)\)
• C) \(- 15 t ^ { 2 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right) - 10 \operatorname { sech } ^ { 2 } \left( \frac { 1 } { t ^ { 2 } } \right)\)
• D) \(- 15 t ^ { 2 } \tanh \left( \frac { 1 } { t ^ { 2 } } \right) + 10 \operatorname { sech } ^ { 2 } \left( \frac { 1 } { t ^ { 2 } } \right)\)

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Definitions:

Diseconomies of Scale

The phenomenon where a company's production costs increase as it produces more, resulting in a decrease in efficiency.

Output Units

Quantitative measures of production, representing the number of units of goods or services produced.

Economies of Scale

Cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output decreasing with increasing scale.

Long-run Average Total Cost

The average cost per unit of output in the long run, where all inputs are considered variable and firms can adjust all factors of production.