Find $f'(x)$ at given value of x Find $f'(x)$ at the given value of x
$f(x)=\sqrt{x+2}$ 
Find $f'(7)$
My question for this one is do I approach this question by trying to find the derivative of the initial equation and then once I have found the derivative do I simply plug in 7 for x and solve?
So once I start solving I would get $\frac{\sqrt{x+h+2}-\sqrt{x+2}}{h}$
$\lim_{h\to0} \frac{\sqrt{x+h+2}-\sqrt{x+2}}{h} = \lim_{h\to0} \frac{\sqrt{x+h+2}-\sqrt{x+2}}{h} \cdot \frac{\sqrt{x+h+2}+\sqrt{x+2}}{\sqrt{x+h+2}+\sqrt{x+2}}$
From that point I would get 
$\frac{(x+h+2-x-2)}{h\sqrt{x+h+2}+\sqrt{x+2}}$

$$f'(x)=\frac{1}{2\sqrt{x+2}}$$
$$f'(7)=\frac{1}{2\sqrt{7+2}}=\frac{1}{6}$$
