Q. 56. - Calculus

Question

For the partial derivatives given in Exercises 55–58, find the

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

with the given partial derivative.

$\frac{\partial f}{\partial y}=0$

Step-by-Step Solution

Answer

The most general form of $f(x, y, z)$so that $\frac{\partial f}{\partial y}=0$is $f(x, y, z)=h(x, z)$

Step 1: Given information

Given derivative is $\frac{\partial f}{\partial y}=0$

Step 2: 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 $\frac{\partial f}{\partial y}=0$

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

Then,

$\frac{\partial f}{\partial y}=0$because $x and z$treated as constant.

Hence the most general form of $f(x, y, z)$so that $\frac{\partial f}{\partial y}=0$is $f(x, y, z)=h(x, z)$