Find the derivative of: y=x^3/2 *(3ln(x)-2)

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Homework Statement



Find the derivative of:

y=x^3/2 *(3ln(x)-2)

Homework Equations



as above

The Attempt at a Solution


iam using product rule
dy/dx =[d/dx x^3/2]*(3ln(x)-2) + x^3/2 [d/dx(3ln(x)-2)]

how to solve ln differential ?
 
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Thank u guys
 

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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