Question

I need help with this one, Find the derivative by the limit process. f(x) = √(x+4). I have the answer but I can't seem to get it using the difference quotient.

Answer 1

\[\frac{dy}{dx}=\frac{f(x-\Delta x)-f(x)}{\Delta x}\]is the formula I am using. The answer is \[\frac{1}{2\sqrt{x+4}}\]We haven't learned the chain rule yet, its in the next chapter.

Answer 2

\[
\lim_{h\to0}\frac{\sqrt{x+4+h}-\sqrt{x+4}}{h}
\]Multiply by the conjugate? That is to say, \[
\frac{\sqrt{x+4+h}+\sqrt{x+4}}{\sqrt{x+4+h}+\sqrt{x+4}}
\]

Answer 3

That's just my first guess, haven't worked it out yet.

Answer 4

Nvm, I found what I did wrong but yea multiplying by the conjugate is probably easier than what I was going. I tried to square both the top and bottom but I didn't do the top right. Thanks