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Chapter 12: Q. 51. (page 944)

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

most general form for a function of two variables, f(x,y), with

the given partial derivative

鈭�f鈭�x=0

Short Answer

Expert verified

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

Step by step solution

01

Given information

Given derivative is鈭�f鈭�x=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�x=0

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

hence,f(x,y)=h(y)

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