Find ∂r/∂x_j: Tensor Problems Explained

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1. find ∂r/∂x_{j}, where r=|\underline{x}|

2. is this the same as differentiating a modulus of a vector?
 
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Try writing r out in components, i.e. r = f(x1,x2,x3,...) and I think it will be obvious what you need to do.
 
phyzguy said:
Try writing r out in components, i.e. r = f(x1,x2,x3,...) and I think it will be obvious what you need to do.

thats what i dunno... what is the component for a mod x?
 
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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