# Math Help - Differentiation

1. ## Differentiation

f(x) = (x) / (1 + |x|)
Show from the definition that f: R -> R is differentiable at 0 and find the value of f'(0)

I have been trying to do it from first principles but keep getting no where.

Any help would be appreciated

2. ## Re: Differentiation

Note that

$f(0)=0$

Using the limit definition. Taking the limit from the right gives

$f'(0)=\lim_{h \to 0^+}\frac{\frac{h}{1+h}-0}{h}=\lim_{h \to 0^+}\frac{1}{1+h}=1$

Taking the limit from the left

$f'(0)=\lim_{h \to 0^-}\frac{\frac{h}{1-h}-0}{h}=\lim_{h \to 0^-}\frac{1}{1-h}=1$