Question

Can someone please briefly write all the derivation rules/laws generally applied in economics while solving equations using derivatives? [ difficulty level: undergraduate intermediate macro]

(Like which terms are treated as constants e.g. automous is treated as a constant but what others?)

Answer 1

The concept of a derivative is extensively used in economics and managerial decision making,especially in solving the problem of optimisation such as those of profit maximisation,cost minimisation,output and revenue maximisation.

RULES

1.Constant Rule - It states that the derivative of a costant function is zero; that is, since a constant function is a horizontal line, the slope or the rate of change of constant function is zero.The derivative a function of the form y=a (where a is a constant) is zero:

dy/dx = 0

2.Power Rule - It states that this derivative is n times the function raised to the (n-10th power times the derivative of the function.To differentiate any function of the form:

y= axⁿ

Where a and n are constant, we take the power n,bring it in front of the function, and then reduce the power by 1:

dy/dx =n*ax^n-1

^{3.Product Rule -We use the product rule or differentiate a function y=uv which is a product of two functions of x,u and v.Tthe product rule says the the derivative of y is :}

^{dy/dx= u dy/dx+v dy/dx}

^{the derivative of aproduct of two functions is the derivative of the first,times the second ,plus the first timest}

^{4. Chain Rule -This rule is used to differentiate a function of another function, y=f(g(x)). It says:}

^{dy/dx=dy/du*du/dx}

^{once you have worked this out ,you replace u by g(x) and your answer is now in terms of x.}