# Math Help - Find f'(x) using the definition of the derivative?

1. ## Find f'(x) using the definition of the derivative?

using the definition of the derivative find:

f(x) = 2 / sqrt(x)

any help is appreciated!

I got stuck right after:

f'(x) = lim (h--> 0) (2/ sqrt(x+h) - 2/ sqrt(x)) / h

I just need to know where to go after this.

Do I find the lcm of sqrt(x+h) and sqrt (x)? What is the lcm and what do I need to multiply both denominators by?

2. Here are the first few steps:

\begin{aligned}
\frac{d}{dx}\left(\frac{2}{\sqrt{x}}\right)&=\lim_ {\small h\rightarrow 0}\frac{1}{h}\left(\frac{2}{\sqrt{x+h}}-\frac{2}{\sqrt{x}}\right)\\
&=\lim_{\small h\rightarrow 0}\frac{2}{h}\frac{\sqrt{x}-\sqrt{x+h}}{\sqrt{x}\sqrt{x+h}}.
\end{aligned}

Hint: What can be done to the second fraction?