Solving Derivatives: Find f'(x) of 6/(z^2+z-1)

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Homework Statement


Find the Derivative of
Code: 
f(x) = [tex]\frac{6}{z^{2}+z-1}[/tex]

Homework Equations


The Attempt at a Solution


Code: 
[tex]6\left(z^{2}+z-1\right)^{-1}[/tex]

Use Chain Rule to conclude
Code: 
[tex]\frac{-12z - 6}{(z^{2}+z-1)^{2}}[/tex]

Is this right?
 
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Yes that is correct.


btw that f(x) should be f(z)
 

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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