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Chapter 1: Q. 1.22 (page 19)

Consider a function f(x1,...,xn)of nvariables. How many different partial derivatives of order rdoes fpossess?

Short Answer

Expert verified

The different partial derivatives of order rthat fpossess arelocalid="1648374000028" n+r-1!(r-1)!n!.

Step by step solution

01

Step 1. State the proposition.

The proposition used here is:

There are n+r-1r-1distinctive non negative integer valued vectors localid="1648373873954" x1,x2,.......,xnsatisfying the equationx1+x2+......+xn=n.

02

Step 1. Find the number of partial derivatives.

The given function f(x1,...,xn)consists of nvariables.

We have to find the partial derivatives of order rpossessed by f.

This means we have to non negative integer valued vectors of x1,x2,.......,xn

Therefore, from the above proposition, the different partial derivatives of order rpossessed by f is given by

n+r-1!(r-1)!n!.

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