How to apply the definition of the derivative of a delta function

rocky3321
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I am supposed to prove that δ'(ax) = (1/a)*(1/|a|)*δ'(x) but I cannot figure out where the (1/a) term comes from. Using the scaling theorem I know that δ(ax) = (1/|a|)*δ(x), but how does this apply to the first derivative and does it explain where the (1/a) comes from?
 
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No need to post any further dialogue because I was able to figure it out. Thanks
 

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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