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