IN PYTHON: please answer all parts

(a) Write a function that takes a list of function values f_i and the spacing dx between them, and returns a list of values for the first derivative of the function. Test your function by giving it a list of known values sin(x) and making a graph for the difference between the output of your function and the expected results.

(b) Make a similar graph as above but instead use for the derivative the Numpy built-in gradient() function.

(c) Write a function that takes a list of function values f_i and the spacing dx between them, and returns a list of values for the second derivative of the function. Test your function by giving it a list of known values for exp(x) and making a graph for the difference between the output of your function and the expected results.

(d) Instead of using the function you have defined for part (c) use 2 times the function you have defined in part (a) for the 1st derivative. Again test your function with exp(x) and plot the difference between the output of your function and the expected results.