Find the derivative of 1/(sqrt(x+2)) using the definition of a derivative

Question

scorcher219396 · Answer

Work so far:

scorcher219396 · Answer

I'm just not sure what to do next?

scorcher219396 · Answer

@Kainui

kainui · Answer

Ahh the trick is to multiply by the conjugate. All that means is you make a fraction that looks like the two square roots on top but with a different sign inbetween. $$\Large \frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}}$$

That will get rid of the square roots on the top allowing you to get rid of your h on the bottom.

scorcher219396 · Answer

So i'm aiming to get rid of the numerator of the numerator? (the top line?)
I was assuming I would need to rationalize the 2nd line

kainui · Answer

The main thing you're trying to get rid of is the h in the denominator because that is essentially dividing by zero and that's what's preventing you from plugging in h=0.

So if you can get an h to show up in the numerator, then it will divide away and you can plug it in safely.

scorcher219396 · Answer

Ok thanks, that makes a lot of sense