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Chapter 12: Q. 56. (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�f鈭�y=0

Short Answer

Expert verified

The most general form off(x,y,z)so that鈭�f鈭�y=0isf(x,y,z)=h(x,z)

Step by step solution

01

Given information

Given derivative is鈭�f鈭�y=0

02

The objective is to find the most general form of a function f(x, y, z) 

The most general form of a function f(x,y,z)so that 鈭�f鈭�y=0

Suppose, f(x,y,z)=h(x,z)

Then,

鈭�f鈭�y=0because xandztreated as constant.

Hence the most general form off(x,y,z)so that鈭�f鈭�y=0isf(x,y,z)=h(x,z)

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