- #1

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## Homework Statement

[tex]\begin{displaymath}

f(x) = \left\{

\begin{array}{lr}

e^{- \frac{1}{x^{2}}} & : x \neq 0 \\

0 & : x = 0

\end{array}

\right.

\end{displaymath} [/tex]

What is the derivative of f(x) at x = 0, that is, what is f'(0)?

## The Attempt at a Solution

I am a bit lost on how to show that f'(0) = 0. I've tried doing it from the definition of the derivative, but then I get

[tex]\displaystyle\lim_{x\to 0}\frac{e^{- \frac{1}{x^{2}}}}{x}[/tex]

and I don't know how to proceed. L'Hôpital's rule doesn't seem to help here, either. Any suggestions?