Derivative of xcos(logx) | Product and Chain Rule Method

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Homework Statement


I want to work out the derivative of xcos(log(x))


Homework Equations





The Attempt at a Solution



By using the product rule: and the chain rule;

cos(logx) - xsin(logx).1/x = cos(log(x)) - sin(log(x))

Is this right?
 
Physics news on Phys.org
looks right
 
buzzmath said:
looks right

Thankyou
 

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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