###  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 : to review geometry, basic trig, and inverse function. to justify the algebraic extression for the Arcfunction. 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 mathnstuff.com   Use inverse.gsp in each level of study.See Arithmetic Stuff: Inverse Math Spoken Here! dictionary definition arc Math Spoken Here! dictionary definition See Precalc Stuff: 3 Problems & Answers set up to first take an inverse graphically then room for algebraically Notes on Inverse Functions including TAKE AN INVERSE VERBALLY Arc and arc functions in the trig topics "Take an Inverse Function in Four Language Families" See Calc Stuff: Inverse functions, derivatives of arc functions (this page) m131Dinverse.pdf Warm-Up on Notes on Taking the derivative of an Inverse function

 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

Review/Recall/Relearn 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 arccosine arctangent arccosecant arcsecant arccotangent

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         © 3/2021, 10/18/2022, 3/12/2023, 10/6/2023, 10/27/2023. A. Azzolino   www.mathnstuff.com/math/spoken/here/2class/420/inverseFX.htm