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Chapter 12: Q. 58. (page 945)

For the partial derivatives given in Exercises 55鈥�58, find the

most general form for a function of three variables, f(x,y,z),

with the given partial derivative.

鈭�2f鈭�y鈭�x=0

Short Answer

Expert verified

The most general form offso that鈭�2f鈭�y鈭�x=0isf(x,y,z)=xh1(z)+zh2(y)

Step by step solution

01

Given information 

Given derivative is鈭�2f鈭�y鈭�x=0

02

The objective is to find the most general form of a function f(x, y, z)  so that ∂2f∂y∂x=0 

Suppose, f(x,y,z)=xh1(z)+zh2(y)

Then,

dfdx=h1(z)+0d2fdydx=0

Hence, the most general form of fso that鈭�2f鈭�y鈭�x=0isf(x,y,z)=xh1(z)+zh2(y)

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