Continuity of arctan x / x at 0.

[mariush]

Homework Statement

f:R->R is defined as f(x) when x\neq 0, and 1 when x=0.

Find f'(0).

Homework Equations

The Attempt at a Solution

Since I can prove that f is continuous at x=0, does that allow me to take the the limit of f'(x) as x-> 0, which is 0? It is quite easy to see that the correct answer must be f'(0)=0, but do i break any rules if I first differentiate f(x) and then look at the limit as x-> 0?

Thanks!

 

[SammyS]

Just use lim_(h→0) (f(x+h)-f(x))/h