derivatives-in-R.Rmd

---
title: "Derivatives in R"
author: "Marie Rivers"
date: "8/3/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(palmerpenguins)
```
## Section 3: Derivatives in R
```{r}
# First Order univariate derivatives
fx <- expression(x ^ 2)
df_dx <- D(expr = fx, 'x')
df_dx
x <- 3
eval(expr = df_dx)

Pa <- expression(2 * (((3 * a) + 2) ^ 4) - 5)
dP_da <- D(expr = Pa, 'a')
dP_da
a <- 1.2
eval(expr = dP_da)

gt <- expression((-4 * t) / (((t ^ 2) + 1)  ^ 3))
dg_dt <- D(expr = gt, 't')
dg_dt
t <- 0
eval(expr = dg_dt)
```

```{r}
# Higher order univariate derivatives
Gz <- expression(4.6 - 1.9 * (z^3))
dG_dz <- D(expr = Gz, 'z')
dG_dz

d2G_dz2 <- D(expr = dG_dz, 'z')
d2G_dz2
```

```{r}
# partial derivatives
f_xyz <- expression(2*x^2*y - 3*x + 1 + 4*z^4*x)
df_dx <- D(expr = f_xyz, 'x')
df_dx

df_dy <- D(expr = f_xyz, 'y')
df_dy

dg_dz <- D(expr = f_xyz, 'z')
dg_dz
```
## Section 4: Make Some Plots
```{r}
eq_fx <- function(x) {
  (2.4 * (exp(-0.05*x)) * sin(x))
}
ggplot(data = data.frame (x = c(-.5, .5)), aes(x=x)) +
  stat_function(fun = eq_fx)
```
```{r}
#### Penguin bill length vs. bill depth
ggplot(data = penguins, aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(aes(color = species)) +
  labs (x = "bill length (mm)",
        y = "bill depth (mm)",
        title = "Palmer penguins bill size",
        caption = "data collected by KB Gorman ey al. at Palmer Station",
        color = "species")
        
  
```
```{r}
ggplot(data = penguins, aes(x = species, y = flipper_length_mm)) +
  geom_jitter() +
  labs (x = "species",
        y = "flipper length (mm)",
        title = "penguin flipper length by species")
```
```{r}
print(hello)
```