What is the differentiation and integration of f(x)=1 wrt dx

If $f(x) = 1$, then the derivative of $f(x)$ with respect to $x$ (denoted as $f'(x)$ or $\frac{df}{dx}$) is zero because the function is constant.

$f'(x) = \frac{d}{dx}(1) = 0$

The integral of $f(x) = 1$ with respect to $x$ (denoted as $\int f(x)dx$) is simply $x$ plus a constant of integration (often denoted as $C$).

$\int 1 \,dx = x + C$

So, in summary: $f'(x) = 0$
$\int 1 \,dx = x + C$

where $C$ is the constant of integration.