Differentiate

this one is actually not such a tough problem as it may have seemed.

You need to first remove the so many radicals (roots) present!

how do you do it? multiplying by the conjugate (not the complex one...)

obviously we will want the denominator to be a simple thing.. bcos it makes our own next step easy.

We will not directly differentiate the whole thing!

(√a+x+√a-x) can be multiplied by (√a+x-√a-x) to give something beautiful.
THat is (a+x)-(a-x) = 2x

so we go ahead and multiply and divide the given thing by this factor!
{(√a+x-√a-x)(√a+x-√a-x)}/{(√a+x+√a-x)(√a+x-√a-x)}

we get
(√a+x+√a-x)²/2x
={a+x+a-x+2√(a+x)(a-x)}/2x
= {a+√(a²-x²)}/x

Now the question is not very difficult! is it!