Basic differentiation, please write so I can read it! Thanks

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Show transcribed image text Basic Differentiation Techniques Module Project In this Module Project we will explore patterns that arise in repeated differentiation. Below you will find three functions. What we are going to do is repeatedly differentiate these functions and try to find a pattern we can use to describe the "nth" derivative. Here are a couple of useful tools for expressing your final results: The factorial of a positive integer n is: so for example, 2! = 2.1.3! = 3-2-1, 4! = 4.3.2.1. Asrm sure you noticed, it is clear that: n!(n-1! An alternating sequence -1,1,-1, 1,-1,may be written as (-1), where n is the number of the termin the sequence starting with n 1, (first term, second term, etc.) For each of the following functions, find a formula for the "nth" derivative of the function. As a means to get started, do this for n = 1 (first derivative), 2 (second derivative) and 3 (third derivative, and maybe even n = 4, then look for a pattern. Leave negative exponents in each derivative in preparation for computing the next one Denote the "nth" derivative as x) a fx)1 b) f(x)=1+x c) f(x)vx d) fx)-e*