Applications of partial derivatives

**Applications of partial derivatives**

In this section we solve problems
on partial derivatives which have direct impact on Industrial areas.

**Production function and marginal
productivities of two variables**

Production *P* of a firm depends upon several economic factors like capital (*K*), labour (*L*), raw materials (*R*),machinery
(*M*) etcâ€¦ Thus *P* = *f*(*K,L,R,M,â€¦*) is known as production
function. If *P* depends only on labour
(*L*) and capital (*K*), then we write *P*=*f*(*L,K*).

Let *P *= *f*(*L,K*) be a production function. Then âˆ‚P/âˆ‚L is called the **Marginal productivity of labour **and** **âˆ‚P/âˆ‚L** **is called the** Marginal productivity of capital.**

Eulerâ€™s theorem for homogeneous
production function *P*(*L,K*) of degree 1 states that

Tags : Applications of partial derivatives , 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation : Production function and marginal productivities of two variables | Applications of partial derivatives

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