Find the Derivative of the Function $$y = \frac { 1 } { 6 } ( 8 x + 10 ) ^ { 3 } + \left( 1 - \frac { 1 } { x ^ { 3 } } \right) ^ { - 1 }$$

question 19

Multiple Choice

Find the derivative of the function.
- $$y = \frac { 1 } { 6 } ( 8 x + 10 ) ^ { 3 } + \left( 1 - \frac { 1 } { x ^ { 3 } } \right) ^ { - 1 }$$

• A) \(\frac { 1 } { 2 } ( 8 x + 10 ) ^ { 2 } - \left( 1 - \frac { 1 } { x ^ { 3 } } \right) ^ { - 2 }\)
• B) \(\frac { 1 } { 2 } ( 8 x ) ^ { 2 } - \left( \frac { 3 } { x ^ { 4 } } \right) ^ { - 2 }\)
• C) \(\frac { 4 } { 3 } ( 8 x + 10 ) ^ { 2 } + \frac { 3 } { x ^ { 4 } } \left( 1 - \frac { 1 } { x ^ { 3 } } \right) ^ { - 2 }\)
• D) \(4 ( 8 x + 10 ) ^ { 2 } - \frac { 3 } { x ^ { 4 } } \left( 1 - \frac { 1 } { x ^ { 3 } } \right) ^ { - 2 }\)

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Definitions:

Elasticity of Demand

A metric that assesses the sensitivity of the demand for a good to shifts in its price level.

Substitutes

Products or services that can be used in place of one another, where an increase in the price of one leads to an increase in demand for the other.

Good A

A term which might refer to a specific product or item in a hypothetical economic scenario or model, but without more context is not a standard economic term.

Good B

An unspecified product referred to for the sake of example; characteristics or qualities would depend on the context.