Help with Derivatives of Cubic Root Function

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Homework Statement



FIND THE DERIVATIVES OF THE FOLLOWING FUNCTION:

CUBEROOT OF ((x^3+1)/(x^3-1))


Homework Equations





The Attempt at a Solution

 
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Well do you know what the chain rule is? quotient rule?

those will probably be pretty useful here.
 
yeah but how do you get rid of the cuberoot
 
Do you know how to take the derivitive of Cuberoot(x)?

or how about cuberoot(x^2)

if not those, how about the square root (x)
 
How do you re-write the cuberoot in exponent form? I think that's what's messing you up.
 
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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