Q. 52. - Calculus

Question

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

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

the given partial derivative

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

Step-by-Step Solution

Answer

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

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 )  

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

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

Hence, $f(x, y)=g\left(x\right)$