what does "derivative" means in image processing? In image processing and especially edge detection, when we apply sobel convolution matrix to a given image, we say that we got the first derivative of the input image, and when applying the laplacian matrix to the initial image we say that we got the second derivative.  

Taking into consideration that in both cases we applied the same operation (img * matrix), then why the first operation gave us the first derivative, and the second one gave us the second derivative and not the fifth ? is the values of the mask (convolution matrix) which decide which derivative we got ? or I'm already mistaken in my description ?
Look at the numbers in the filter kernel in just 1 dimension for simplicity. For a Sobel and  Prewitt matrix you have something that roughly looks like this 

[-1,0,1]. 

Convolving this with your image basically computes the difference between the pixel values of the neighboring pixels. You apply 0 to the current pixel, 1 to the pixel on the right and -1 to the pixel on the left. This gives a first order difference: 

next pixel - previous pixel, 

i.e. first derivative.

But now look at a Laplacian operator. It looks something like [1, -2, 1]. This computes the difference of differences. To see how, note that

[1,-2,1] corresponds to

next - 2 x current + previous

i.e.

next - current - current + previous

i.e.

(next-current) - (current-previous)

Now notice how this is a diference of differences. (next - current) is like a 1st derivative. (current - previous) is like 1st derivative. Their difference is like a 2nd derivative.