This applet can be used to induce the relationship between the derivative of a function at a point and the derivative of the inverse of the function at the corresponding point.

1. How are the functions y=sin^2 and y=arcsin(x) related?
Use the slider tool to answer the following questions.
2. What is the slope of y=sin^x at the point (0, 0)? What is the slope of y=arcsin(x) at the point (0,0)? How are the slopes related?
3. What is the slope of y=sin^x at the point (pi/2, 1)? What is the slope of y=arcsin(x) at the point (1, pi/2)? How are the slopes related?
4. What is the slope of y=sin^x at the point (pi/4. Sqrt(2)/2)? What is the slope of y=arcsin(x) at the point (sqrt(2)/2, pi/4)? How are the slopes related?
5. Based on your observations from questions 2 through 4, make a conjecture about the derivative of a function f at a point (a, b) and the derivative of the inverse of f, g, at the corresponding point (b, a).