calc1   Inverse Functions & Their Derivatives -- Think "The Derivative of an Arc Function"

Thoughts of and for the Past, Present, & Future

    Many ideas are addressed here.

    At present, in the course outline written by the math department and in the textbook chosen for the course, the topic is "Derivatives of Inverse Functions." So, with the text you will be taking derivitives of inverse trig functions. This page is more for the math which "entitles" the student to use the arcfunction derivatives listed in the table because they have "earned" their use through study. This page also facilitates the "harvesting" of material for the assigned Test Summary.

    From the past, one must know basic Pythaghorean Theormem geometry, basic "Oscar Had A Heap of Apples" trig, inverse functions, and the derivatives of the trig functions you learned earlier in the course.

    In the future, the antiderivatives of the arcfunctions should be obvious.

    In short the page is :
  1. to review geometry, basic trig, and inverse function.
  2. to justify the algebraic extression for the Arcfunction.
  3. to take the derivative of Arcfunctions, derive the derivative formula.

    It is left for the reader to find another source for problems on using an arcfunction derivative formula for taking the derivative.

Related Stuff on   Use inverse.gsp in each level of study.
    See Arithmetic Stuff:
  • Inverse Math Spoken Here! dictionary definition
  • arc Math Spoken Here! dictionary definition

Dowload inverse.gsp - Sketchpad of inverse functions
    0 - vertical, horizontal line tests
    1 - square root fx
    2 - any function
    3 - sqrt fx by parameters
    4 - restricted domain on inverse    
    5 - arcsine
    6 - arctangent
    7 - f and inverse
    8 - f, inverse, tangents

Download Geometer's Sketchpad for Free!


Oscar Had A Heap Of Apples
Short Answers
Long Review
Long Answers
New and/or Expanded Ideas -- Derivatives of Trig Functions & Arc Functions

      a square root function w/ text
a square root function w/o details
the sine function w/ details
the sine function w/o details


Summary & Anti-derivatives

Dowload absement.gsp Use sheet 14 & 15
    0 - toc
    1 - time, t
    2 - displacement, distance, s(t)
    3 - definition of derivative
    4 - s(t), s'(t)
    5 - s(t), s'(t), s''(t)
    6 - emojis, f, f', f'', tangent line
    7 - trace derivatives
    8 - PARTITION & SUMS 4 boxes
    9 - Reimann & Sums
    10 - SUMS absement, input [a,b]
    11 - absement, n=32
    12 - absement plus c
    13 - play absement plus c
    14 -arcsine actual fx graphed
    15 - arcsine mesh - useF(x) plot to plot arcsine

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