Derivative of 4/sqrtx Using the Limit Process

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Homework Statement


Find the derivative of 4/sqrtx using the limit process

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The Attempt at a Solution



I know the method and I even know the answer using other (easier) means but I just cannot simplify it. I've tried almost everything i can think of. I feel like this is an easy answer but I'm just not seeing it.

I tried rationalizing the numerator and that helps me with taking the actual limit but I'm having problems simplifying to the correct answer.
 
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Show us what you tried and we'll help you with this problem.
 
Never mind, like I said easy problem just couldn't see it.

Ate lunch and came back to it and it all made sense. Thanks anyway
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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