1. Let's clarify the question: it seems you are asking why or how the differential operator $d\!u$ might disappear in a mathematical context. 2. The differential $d\!u$ represents an infinitesimal change in the variable $u$. It "disappears" or is omitted in certain contexts, such as when performing substitution in integrals or when expressing derivatives. 3. For example, in integration by substitution, if $u = g(x)$, then $du = g'(x) dx$. When changing variables, the integral changes from $\int f(x) dx$ to $\int f(g^{-1}(u)) \frac{dx}{du} du$, and the $du$ is essential to represent the variable of integration. 4. However, in derivative notation like $\frac{dy}{dx}$, the $d$'s are part of the notation and not separate quantities; they don't "disappear" but are symbolic. 5. In some algebraic manipulations, differentials may be canceled or simplified, but this is a formal process justified by the rules of calculus. 6. If you provide a specific example or context, I can explain precisely why $d\!u$ disappears or is omitted there.