Exploring Derivatives

An applet for looking at derivatives of various functions.
1. How does the function f'(x) change as the function is animated? 2. Uncheck show f'(x). How does the shape of f'(x) compare to the shape of f(x)? 3. Change f(x) to be sin(x) what is the function f'(x) equal to? 4. Change f(x) to be x^2 + 3. What is the degree of x^2 + 3? What is the degree of f'(x)? 5. Change f(x) to be x^3. What is the degree of f'(x)? What is the relationship of the degrees of f(x) and f'(x)? Do you think this is always the case?