Given a Vertical Derivative Kernel, Find the output image after K is applied to the above input image
Read about convolution here. The link has a web tool to understand convolution better. That will help you. Here is a quick primer on how to go about solving your problem.



You have to choose a pixel, place kernel such that centre of kernel is on the pixel you want to compute. Multiply the overlapping pixels and dive by number of non-zero pixels as shown above. For the boundary pixels you have to take a call as to what you will do. There are many options like use zeros as boundary etc. For derivatives it is better to keep the boundaries as zero. Hope this helped you :)