How Accurate Is the Logarithmic Differentiation in This Example?

Ry122
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Question:
Find derivative of f(x)=((x^2)(x^3))/((x^4)(x^2))
Attempt:
ln f(x)=(lnx^2)+(lnx^3)-(lnx^4)-(lnx^2)
Can someone tell me what I have done wrong so far?
Thanks
 
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forgot to take log of both sides?

bring your powers down.. oo well, u prolly know this
 
Why don't you just simplify and then differentiate?
 
I did take the log of both sides. I'm doing it this way because i need to learn this method of differentiation.
 
oo yep, just realized that.
everything looks good
 

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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