Differentiate the Following Functions:
(A) $f ( x ) = ( \ln x ) ^ { 3 }$

question 24

Essay

Differentiate the following functions:
(a) $f ( x ) = ( \ln x ) ^ { 3 }$ (b) $f ( x ) = \sqrt { x } \ln x$ (c) $f ( x ) = \ln \left( \frac { \tan x } { x ^ { 2 } + 1 } \right)$

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Definitions:

Long-Run Cost Function

A graphical or mathematical representation that shows the lowest cost at which a firm can produce any given level of output in the long run, when all inputs are variable.

Positive Output

A situation where the production of goods or services is above zero.

Production Function

An equation or system that illustrates the connection between production inputs and the resulting products or services.

Long-Run Total Cost

Refers to the total cost incurred by a firm in producing a given output when all inputs, including both fixed and variable costs, are considered over a longer period.