While this particular question is from a calculus class I'm taking, this issue has plagued me for some time; I simply didn't care enough to bother figuring it out. Now, however, it'll cost me if I don't get it, so I'd like to know how to simplify something like this:
$$\frac{\sqrt{2a + 2h + 1} - \sqrt{2a + 1}}{h}$$
This particular problem is attempting to find the derivative of $\sqrt{2x+1}$ (using limits, not just doing the derivative). So, one finds the derivative using limits through the limit as $h \to 0$ of $\frac{f(a+h)-f(a)}{h}$. However, when I put in the function $\sqrt{2x+1}$, I get the above expression. Is there a way to simplify this (and other difficult square roots) or am I just doing this wrong?
Thank you!
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