Section 1: (Small groups) Derive the definition of the derivative

  • Put all notes away
  • With a partner, based on what you’ve learned, derive the definition of the derivative from scratch
  • At every step, describe what you are doing
  • Once you have the definition of the derivative, say out loud (each person) what we’re doing mathematically every time we find the derivative

[SKIP] Section 2: Derivatives by hand

  1. By hand and using derivative rules: Find \(\frac{dx}{dt}\) for \(x(t)=\frac{1}{x^3}+2.4e^{3x}\)

Section 3: Derivatives in R

  • Create a new Quarto Project (named eds-212-day-2) (or using a naming convention you choose for all EDS 212 projects)

  • Create a new Quarto document in the project

  • Attach the tidyverse and palmerpenguins packages with library(package_name) (note: you may need to install palmerpenguins - remember install.packages("packagename"))

  • Render (save your .qmd as eds212_day2_activities.qmd, or follow a naming convention you’ve decided on)

  • Use usethis::use_git() and usethis::use_github() to make your project a version-controlled repo, with an upstream GitHub repo

  • In your Quarto document, find the derivative expression and slope at the indicated value for each the following functions in R (each in a separate code chunk).

    1. Find the slope of \(f(x)=x^2\) at \(x = 3\)
    2. Find the slope of \(P(a)=2(3a+2)^4-5\) at \(a = 1.2\)

  • Render, then stage, commit, pull, then push your changes to your repo on GitHub. Check your repo (refresh) to make sure the changes show up there.

Section 4: Make another penguin plot

  • In a new code chunk, create a ggplot graph of penguin bill length versus bill depth (using the penguins dataset in the palmerpenguins package), with point color dependent on species. You should attach the tidyverse and palmerpenguins package in your .qmd setup chunk if you haven’t already. Update labels and add a title.

  • In a new code chunk, make a jitter plot of flipper length by species (species on the x-axis, flipper length on the y-axis). Update axis labels and add a title. See ?geom_jitter

  • Render your .qmd to check for reproducibility

  • Stage, commit, and push changes to the remote repo. Once you do, go to GitHub and check to see the changes are safely stored & tracked.

  • Go back to your Quarto document in RStudio. Pull to make sure you have the same versions as in the remote repo. Make a change (anything you want - maybe change your graph colors, sizes, etc.), then stage, commit, & push changes to the remote repo to reinforce the steps. Check that changes are stored on GitHub.

  • Repeat one more time - make a change to your plot, knit, stage, commit & push. Check that your changes appear on GitHub.

End