Looking for a hint about kernel exercises

First of all, I thank you for providing this awesome online book for free. I would like to ask some questions that I couldn’t figured out.
Questions on are as below:
1.Design some kernels manually.

  • What is the form of a kernel for the second derivative?
  • What is the kernel for an integral?
  • What is the minimum size of a kernel to obtain a derivative of degree d?

For the first question, is this question simply asking the shape of a kernel for second derivative? So, it’s the same shape of the previous input shape just like the shape of a kernel for first derivative (each partial derivative of the output with respect to weight in kernel)?
For the second and third question, I have no idea. Is there any article that you suggest me to read for this exercise?