can you please create a python script that outputs a derivative using The Average Rate of Change Formula A(x) = f(b)-f(a) /(b-a) when x is user input

Of course ! I ' d be happy to help you with that . \n To create a Python script that outputs the derivative of a function using the A verage R ate of Change formula , you can use the following code : \n ``` \n import math \n def derivative ( f , a , b , x ): \n # Calcul ate the difference quot ient \n diff = f ( b ) - f ( a ) \n # Calcul ate the ratio of the difference quot ient to the difference \n ratio = diff / ( b - a ) \n # Return the derivative \n return ratio \n \n # Example usage \n \n x = float ( input (" Enter a value for x : " )) \n f = lambda x : x ** 2 \n a = 0 \n b = 2 \n der iv ative ( f , a , b , x ) \n print (" The derivative of f ( x ) = ", f ( x ), " is ", derivative ( f , a , b , x )) \n ``` \n In this code , the ` der iv ative ` function takes in four arguments : ` f `, ` a `, ` b `, and ` x `. It first calcul ates the difference quot ient by subtract ing ` f ( a )` from ` f ( b )` and storing the result in ` diff `. Then , it calcul ates the ratio of the difference quot ient to the difference between ` a ` and ` b `, and stores the result in ` rat io `. Finally , it returns the derivative of ` f ( x )` as the ratio of ` diff ` to the difference between ` a ` and ` b `. \n In the example usage , we define a simple function ` f ( x ) = x ** 2 `, and then call the ` der iv ative ` function with ` a = 0 `, ` b = 2 `, and ` x ` as an input from the user . The output will be the derivative of ` f ( x )`, which is ` 2 x `. \n I hope this helps ! Let me know if you have any questions or need further assistance . </s>