improc ass4: Added proof of separability Gaussian derivatives.

improc/ass4/report/report.tex

@@ -154,8 +154,16 @@ We can show analytically that all derivatives of the 2D Gaussian function
 are separable as well:
 
 \begin{table}[H]
-	\begin{tabular}{rl}
-		$ $ & $= $ \\
+	\begin{tabular}{rll}
+		$ \frac{\delta}{\delta x} \frac{\delta}{\delta y} G_{2D}(x, y)$
+		& $= \frac{\delta}{\delta x} (\frac{\delta}{\delta y} (G_{1D}(x)
+            \cdot G_{1D}(y)))$ & $G_{2D}(x, y) = G_{1D}(x) \cdot G_{1D}(y)$ is
+            given \\
+		& $= \frac{\delta}{\delta x} (G_{1D}(x) \cdot
+		    \frac{\delta}{\delta y} G_{1D}(y))$ & because $G_{1D}(x)$ is
+		    constant with respect to $y$ \\
+		& $= \frac{\delta}{\delta x} G_{1D}(x) \cdot
+            \frac{\delta}{\delta y} G_{1D}(y)$ & \\
 	\end{tabular}
 \end{table}