Differential of a Function
The differential of a function y = f(x) measures how the function f(x) changes in response to an infinitesimal change in the independent variable x. $$ dy = f'(x)\, dx $$
Here, dx represents an infinitesimal increment of the variable x.
Meanwhile, f'(x) denotes the first derivative of the function y = f(x).
A Practical Example
Consider the differential of the function y = x2:
$$ dy = y' \, dx $$
$$ dy = D[x^2] \, dx $$
The first derivative of the function is D[x2] = 2x.
$$ dy = 2x \, dx $$
This expression represents the differential of the function y = f(x) with respect to an infinitesimal change in the independent variable x.
And so on.
