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July 6th, 2014, 02:01 PM  #1 
Newbie Joined: Jul 2014 From: denver Posts: 1 Thanks: 0  problem with simplification when taking the derivative of a derivative
edit... solved it by just working through it slowly.... So, first off ty to wheoever reads this, this is my first post so I didn't know whether to put this in the algebra forum, the calculus forum or some other forum. I'm getting confused in some of simplification in one of my calculus homework problems. I'm meant to get d''/x'' of 15x + y^2 = 2 First taking the derivative I get y'= 15x/y, and so far so good. When plugging the derivative in the second time using the quotient rule and plugging in 15x/y for y' it becomes 15y  (15x)(15x/y)  y^2 This somehow simplifies to 15(y^2+15x^2)  y^3 The book skips the simplification in going through the answer so I don't know the steps they took to simplify. I thought the y in 15x/y would only go to the bottom of the fraction so how does 15y become 15y^2? or did the book multiply both top and bottom by y to get rid of the y in 15x/y, but in that case wouldnt the x take on a y as well and we'd get 15(y^2 + 15x^2 * y)  y^3 Last edited by lackofimagination; July 6th, 2014 at 02:08 PM. 
July 6th, 2014, 08:05 PM  #2  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
(15x)(15x/y)*y = (15)(15)(x)(x/y)*y = + $\displaystyle (15)(15)(x)\dfrac{x}{y}*y \ = $ + $\displaystyle (15)(15)x^2$  In general, with three numbers, a, b, and c, (a)(b)(c) = (a*b)(c) or (a*c)(b) or (b*c)(a). But, for instance, (a)(b)(c) $\displaystyle \ \ne \ (a*b)(a*c).$  

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algebra, derivative, double derivative, problem, simplification, taking 
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