Expert: David Hemmer - 7/29/2007

Question
Hi david, this is a first year undergraduate question from a calculus paper, just  having trouble with it, any insight/direction appreciated.
Cheers

Using the limit definition, calculate the derivative adn then find the values of the derivatives specified.

g(t) = 1/t^2;   g'(-1), g'(2), g'(sqrt3)

Answer
g'(t)=-2/t^3.

I assume you can plug in -1, 2 and sqrt3. So let's figure out how to get g'(t) from the definition.

g'(t)=lim_h->0 g(t+h)-g(t)/h

=lim (1/(t+h)^2 - 1/t^2)/h

Now take the numerator and put it over  a common denominator of (t+h)^2t^2 and let h->0. Ask me afollowup if you can't get it from there.