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




Trig Reference Image


[MC,i. Home] [Words] Classes spread sheet notes calc1

© 3/2021, A. Azzolino
  www.mathnstuff.com/math/spoken/here/2class/420/inverseFX.htm