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

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.

Tags : Applications of Differentiation , 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 : Successive partial derivatives | Applications of Differentiation

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