Partial derivatives with constrained variables

jimbo71
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Homework Statement


x^2+y^2=r^2
y-rcos(pheta)
find (partialy/partialr)subscribt phetal, find (partialy/partialpheta)subscribtx, and find (partialy/partial)subsribt pehta


Homework Equations


im not sure how to write this partial in chain rule form. i think the first one (partialy/partialr)subscritpheta would simply be cos(pheta). however i have no idea how to write out the chair rule forumulas for the second and third one. please help




The Attempt at a Solution

 
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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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