July 22nd, 2014, 08:42 PM  #1 
Newbie Joined: May 2014 From: Texas Posts: 8 Thanks: 0  finding derivative
I need help finding the derivative of f(x)=(x2)/((x^2x1)^2) book says its 3(x^23x+1)/((x^2x+1)^3) i understand the quotient rule and finding those derivatives, I don't think I understand the algebra and factoring. Thanks 
July 23rd, 2014, 07:26 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1545 
I disagree with the "book" answer ... check the original f(x) $\displaystyle f'(x) = \frac{(x^2x1)^2  (x2) \cdot 2(x^2x1)(2x1)}{(x^2x1)^4}$ $\displaystyle f'(x) = \frac{(x^2x1)[(x^2x1)  (x2) \cdot 2(2x1)]}{(x^2x1)^4} $ $\displaystyle f'(x) = \frac{(x^2x1)[(x^2x1)  (4x^210x+4)]}{(x^2x1)^4} $ $\displaystyle f'(x) = \frac{(x^2x1)[3x^2+9x5]}{(x^2x1)^4} $ $\displaystyle f'(x) = \frac{3x^2+9x5}{(x^2x1)^3} $ 
July 23rd, 2014, 08:03 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,156 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
If the denominator of $\displaystyle f(x)$ is $\displaystyle (x^2x+1)^2$ instead of $\displaystyle (x^2x1)^2$ then the answer in the textbook is correct.


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