Computing the derivative from the definition Using the limit definition of the derivative which I know is:
$$f'(x)=\lim_{h\to0}\left(\frac{f(x+h)-f(x)}{h}\right)$$
I am trying to solve this problem 
$$f(x)= \frac{x}{x+2}   $$
How do I go about properly solving this, I seemed to get  

$$\frac{x}{x+2}\   $$
  as my answer again? What are the steps I should follow?

I am trying to find the derivative of $f(x)= \frac{x}{x+2}$ using the definition of the derivative. 

$f(x) = \frac{x+2 - 2}{x+2} = 1 - \frac{2}{x+2}$
$$\frac{f(x+h) -  f(x)}{h} = \frac{\frac{2}{x+2} - \frac{2}{x+h+2}}{h} = \frac{2}{h} \cdot \frac{x+h+2 - (x+2)}{(x+2)(x+h+2)} = \frac{2}{(x+2)(x+h+2)} \xrightarrow{h\to 0} \frac{2}{(x+2)^2}$$
