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Applications of Differentiation - Successive partial derivatives | 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

Chapter: 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

Successive partial derivatives

Consider the functionu u = f( x, y) .

Successive partial derivatives

Consider the functionu u = f( x, y) . From this we can find  are functions of x and y, then they may be differentiated partially again with respect to either of the independent variables, (x or y) denoted by .

These derivatives are called second order partial derivatives. Similarly, we can find the third order partial derivatives, fourth order partial derivatives etc., if they exist. The process of finding such partial derivatives are called successive partial derivatives.

If we differentiate u = f(x,y) partially with respect to x and again differentiating partially with respect to y, we obtain .

Similarly, if we differentiate u = f(x,y)  partially with respect to y and again differentiating partially with respect to x

NOTE

If u(x,y)is a continuous function of x and y then


Homogeneous functions

A function f(x,y) of two independent variables x and y is said to be homogeneous in x and y of degree n if f (tx , ty ) = t n f ( x, y) for t > 0.

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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation


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