Q. 51. - Calculus

Question

For the partial derivatives given in Exercises 51–54, find the

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

the given partial derivative

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

Step-by-Step Solution

Answer

The required answer is $f(x, y)=h\left(y\right)$

Step 1: Given information

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

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

Assume that $f$is merely a function of $y$,Taking the partial derivative of $f$with respect to $x$, the function of $y$is assumed to be constant, and the partial derivative with respect to $x$is therefore zero.

hence, $f(x, y)=h\left(y\right)$