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

Pre Derivatives of Inverse Functions Review
1. State/Write
a. the symbol for the inverse of f(x). _______________________
b. the inverse of x squared. _______________________
c. the inverse of raising to a power. _______________________
d. the inverse of taking a log. _______________________
e. the meaning of square root of 25. _______________________
f. the meaning of log (100). _______________________
g. the symbol(s) for "the reciprocal of m". _______________________
h. the symbol(s) for "the reciprocal of the derivative of f(x)". _______________________ 2. Think: Oscar Had A Heap of Apples
a. state the sin(x). _______________________
b. using the triangle given, what is sin(y)?. _______________________
c. what is the length of the missing side?. _______________________
d. using the triangle given, what is cos(y)?. _______________________
e. using the triangle given, what is tan(y)?. _______________________
3. State:
 a. Dx(sin(x)) _______________ b. Dx(cos(x)) _______________ c. Dx(tan(x)) _______________ d. Dx(csc(x)) _______________ e. Dx(sec(x)) _______________ f. Dx(cot(x)) _______________ 4a. Write in symbols: The derivative of an arc function g(x) at (b, a) is the reciprocal of the derivative of the function f(x) at (a, b). 4b. Write in symbols: The derivative of a function f(x) at (a, b) is the reciprocal of the derivative of the arc function g(x) at (b, a).   See Arithmetic Stuff: Inverse Math Spoken Here! dictionary definition arc 3 Problems & Answers set up to first take an inverse graphically then room for algebraically See Precalc Stuff: Notes on Inverse Functions including taking in inerse function verbally Arc and arc functions 3 Problems & Answers set up to first take an inverse graphically then room for algebraically 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 inverse.gsp - Geometer Sketchpad of inverse functions # Trig Reference Image         © 3/2021, A. Azzolino   www.mathnstuff.com/math/spoken/here/2class/420/inverseFX.htm