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Project 2 Task 2.Rmd
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Project 2 Task 2.Rmd
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---
title: "Project 2 Task 2"
author: "Brandon Ritchie"
date: "11/17/2021"
output: html_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
In this project we will take the derivatives and partial derivatives of a few of these likelihood functions. All of these were done on a whiteboard and their images are attached.
## Likelihood Function 1
The first derivative of this function is as follows:
The second derivative of this function is as follows:
## Likelihood Function 4
This function is in 5 parts because there are two variables. As a result a partial and second partial is performed for both $a_1$ and $a_2$ as well as a partial of $a_1$ with respect to $a_2$.
The first partial with respect to $a_1$ is the following:
The first partial with respect to $a_2$ is the following:
The second partial with respect to $a_1$ is the following:
The second partial with respect to $a_2$ is the following:
And finally, the partial of $a_1$ with respect to the partial of $a_2$ is the following:
## Likelihood Function 5
For this function both a first and second derivative were taken with repect to $a_1$. Both are given in the image below:
