Question

use the limit definition of the derivative to find f'
a. let f(x)= 1/(x^2)
b. let f(x)= x^4
c. let f(x)= 9(3√(x^2)

Answer 1

(a) is clearly explained at

http://tinypic.com/view.php?pic=15qynhv&s=4#.VO_LNywYFvA

You can probably find the others as well. Usually the Binomial Theorem is involved.

For instance,

(b) f(x+h) - f(x)
= (x+h)^4 - x^4
= x^4+4x^3h+6x^2h^2+4xh^3+h^4 - x^4
= 4x^3h+6x^2h^2+4xh^3+h^4

Now divide that by h, take the limit, and all the h stuff disappears, leaving you with 4x^3