MAT131 Fall 2025 Notes
mathnstuff.com/math/calc/MAT131fa25/c.13.htm
© 7/12/2025, A2, Agnes Azzolino
Derivatives of Inverse Functions (2.7, pg. 122) & Inverse Functions Review

Welcome to Calc I!
Arc Functions Are Inverse Trig Functions
Hi,
    To best understand the calculus involved in "Derivatives of Inverse
Functions," a good review of inverse functions is needed.
    If you don't need a review, start with the "fake quiz".
    If you have time left to study, go on to the
forshadowing of the antiderivatives of arc functions".
    Contact me through the pink box on www.mathnstuff.com/math/math.htm
    Stay safe, A2
Today's Tasks
1st: (If needed) Start with Basic Precalc:
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.
2nd:
    Today's calc I, on this page is :
  1. to review geometry, basic trig, and inverse function. (This precalc is needed for the calc.)
    Print/use # 5. Pre Derivatives of Inverse Functions Review (also shown at the left)
    Warm-Up on Notes on Taking the derivative of an Inverse function
  2. to justify the algebraic expression for the Arcfunction.
    (Basic vocabulary helps understanding of new material.)
  3. to take the derivative of Arcfunctions, derive the derivative formula. (the meat of today's content)
    More Advanced calc I, tomorrow's calc: the antiderivatives of the arcfunctions should be obvious.
    Summary & Anti-derivatives