I am trying to calculate some thing called directional derivatives of a vector b (which defined in attached file as an example)
to calculate the directional derivatives of the vector b .
the result of the example is also in the attached file.

I serached in goolge to find how we can calculate the directional derivatives, but I could not find any function in python to do this kind of calculation ; the only thing I found which do derivative in python is:

scipy.misc.derivative(func, x0, dx=1.0, n=1, args=(), order=3)

this function dose not give me the right answer .

Could you please help me to solve this probelm.
the example

this calculation I can easly do it by hand. But I could not find a way to do it in python ?
I appreciate your help