Problem involving derivative and left-hand limit

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This is from an online homework that's due in an hour. This question has been bothering me all day and I'm convinced that there's a problem with the website.

It's asking for the expression that's used to find the left-hand limit of the derivative, f'(0).

It won't take 2x+6 as the answer... Am I missing something or is the website just screwed up?

I attached a picture of the problem. Help fast!
 

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Do you remember the derivative of of $$x^n$$?
 
Wouldn't that be n?
 

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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