How do u implicitly differentiate (xy)^1/2

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Homework Statement



How do u implicitly differentiate (xy)^1/2

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The Attempt at a Solution



Would it be 1/2(xy)^-1/2 multiplied by 1 and dy/dx. Thanks
 
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It looks like you are trying to use the chain rule so you are on the right track. What's d/dx of xy? BTW, so far, this isn't implicit differentiation.
 
what do u mean it isn't implicit differentiation?
 
It's just differentiation. Implicit differentiation is where you take d/dx of an equation and then solve for dy/dx. There's no equation yet. And you haven't answered my question.
 

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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