1. The problem statement, all variables and given/known data Is the operator Lu = du/dx + u * du/dy linear? 2. Relevant equations Linearity occurs for L[u+cv] = L + cL[v] 3. The attempt at a solution I know this isn't linear because of the second term, but I don't understand why I can't write the operator as L = (d/dx + u * d/dy) which then seems to almost work out, except that I don't know what to make 'u' in the operator when applying the linearity condition since the linearity condition uses two different functions instead of only 'u'.