For each of the following operations, obtain a $3$ x $3$ separable filter kernela$-)1$st order derivative operation on x$-$direction and $2$d order derivative operation on j$-$directionb$-)2$ order derivative operation on x$-$direction and Prewitt type averaging operation on y$-$directionc$-)$ Sobel type averaging operation on x$-$direction and a summing of $3$ consecutive pixels on y$-$direction $($Hint: it sums three consecutive pixels and write the result to the position of the centre pixel on the output image$)$