Weak derivative
= Weak derivative
{wiki}
A locally integrable function $g$ is the $i$th weak derivative of $u$ when
$$
\int_UuD_i\varphi=-\int_Ug\varphi
$$
for every <test function> $\varphi\in C_c^\infty(U)$. Thus a weak derivative is a <distributional derivative> that is represented by a locally integrable function.
= Generalized derivative
{synonym}