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Chapter 12: Q. 52. (page 944)

For the partial derivatives given in Exercises 51鈥�54, find the

most general form for a function of two variables, , with

the given partial derivative

鈭�f鈭�y=0

Short Answer

Expert verified

The required answer isf(x,y)=g(x)

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) 

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

Assume that fis merely a function of x. When the partial derivative of fwith respect to yis calculated, the function of xis assumed to be constant, and the partial derivative with respect to yis zero.

Hence,f(x,y)=g(x)

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