Demand Function: \({ Q }_{ d }=f\left( { P }_{ x } \right) \) Where "Q_d" stands for Quantity demand of a commodity and \(\left( { P }_{ x } \right) \) is the price of that commodity.
Supply Function: \({ Q }_{ s }=f\left( { P }_{ x } \right) \) Where  "\({ Q }_{ s }\)" stands for Quantity supplied of a commodity and \(\left( { P }_{ x } \right) \) is the price of that commodity.

\(I=\int { \left( { 4x }^{ 5 }+6{ x }^{ 3 }+\frac { 2 }{ 3 } x \right) } dx\)
\(=4\left[ \frac { { x }^{ 6 } }{ 6 } \right] +6\left[ \frac { { x }^{ 4 } }{ 4 } \right] +\frac { 2 }{ 3 } \left[ \frac { { x }^{ 2 } }{ 2 } \right] +c\)
\(I=\left( \frac { { 2x }^{ 5 } }{ 3 } +\frac { { 3x }^{ 4 } }{ 2 } +\frac { { x }^{ 2 } }{ 3 } \right) +c\)

Marginal product of a factor of production refers to addition to total product due to the use of an additional unit of a factor
MP = d(TP) / dQ = ΔTP /ΔQ

It is used in data analysis by using formula. A spread sheet is a large sheet of paper which contains rows and columns. The intersection of rows and columns is termed as 'cell'. MS Excel 2007 version supports up to 1 million rows and 16 thousand columns per work sheet.

Marginal Revenue is the revenue earned by selling an additional unit of the product. In other words, Marginal Revenue is an addition made to the total revenue by selling one more unit of the good.
MR= \(\frac { d\left( TC \right) }{ dQ } \) (or)  = \(\frac { \triangle \left( TC \right) }{ \triangle\ Q } \)
Where ΔTR stands for change in the total revenue, and ΔQ stands for change in output.