Originally Posted by

**ScottO** I came across this question in one of my old textbooks:

If the function y = f(x) has domain D and its derivative y' = f'(x) has domain D', what can one say about the relative sizes of D and D'?

After a bit of thought, I found 3 examples having D < D', D = D', and D > D':

$\displaystyle y = x^x \rightarrow y' = x^x (\ln x + 1)$

$\displaystyle y = x^2 \rightarrow y' = 2x$

$\displaystyle y = \ln x \rightarrow y' = \frac{1}{x}$

So, is the answer, it depends? Or am I missing something?

-Scott