Posted by Joel on September 23, 2002 at 17:56:06:
In Reply to: really quick help posted by sean on September 23, 2002 at 16:08:58:
: what is the derivative of 1/x² ?
: i keep getting lost in all the x and h garbage. i get to (x²-x²-2hx-h²)/[x²(x²+2hx+h²)] and then i get a bit confused. is that much even right?
but you lost an h.
(x²-x²-2hx-h²)/[hx²(x²+2hx+h²)] remember, in the definition of a derivative you started out with h as the denominator.
Now, the x²-x² becomes 0 and you factor -2hx-h² into -h(h+2x). The h in the numerator cancels the h I just put back into the denominator, so you're left with:
and I'm sure you can take it from there.
The answer, as you will see in VM's post, is -2/x^3.
Your question should have stated: "Using the definition of a derivative, what is the derivative of 1/x^2?
Post a Followup