Calculating Partial Derivatives of a Multivariate Function at a Point

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Homework Statement



Calculate the derivative of f(x,y,z)=(\frac{z^3}{y} , \frac{x^3}{z}) at (1,2,3)

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The Attempt at a Solution



Okay guys and gals, this problem was on my final today. It was the only problem I had a gutsy but unsure feeling about. The actual answer itself does not matter to me, rather the concept of understanding is.

I basically interpreted the problem this way:

Find the partial derivatives with respect to x,y,z for the two functions of f. So it is a 2 x 3 matrices. Plug in the points and you are done.

Did anyone else get this interpretation of the problem/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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