Khan/khan-exercises — Issue #6182: Quotient rule - Video method does not match the exercise result
Author: KhanBugz
Created: 2011-11-12 23:01:01+00:00
State: open
Labels: firefox, win7

Reporter: Nicholas.Mark.Kolesar@gmail.com

This is an issue where the way in how to solve the problem shown in the video is different then how the exercise solves and simplifies the problem...

I started trying to do this problem, the way that was shown in the Quotient Rule video. Which was to change sin(x)/(-x)^2 into sin(x) * (-x)^(-2).

I then proceeded to differentiate how it shows in the vide0:

cos(x) * [(-x)^(-2)] +
-1 * [(-2x)^(-3)] * sin (x)

For me, this simplified to [2*sin(x) / x^3] - [cos(x) / x^2]

However this was not one of the answers available. I double checked my work with a TI-89 calculator and it gave me the same answer in the simplified formatted I just notated above.

After playing around with the calculator, I found the answer that the exercise expects:

[((cos(x)*(-x^2))-((-2x)*sin(x))] / (-x^2)^2

simplified in the calculator to [-(x*cos(x)-2*sin(x))] / x^3.

... So i did one more comparison to see if the answer i arrived to first = the answer the exercise expected and received a binary "true" saying the expressions were technically equivalent.

Ok. So that's a long way around to show that both answers are correct. The point though is that my formatted answer was arrived by using the method shown in the "Quotient Rule" video, which resulted in something that would not easily be simplified or associated with the method and syntax the exercise expected you to find.

There was no mention in the video of the f′(x)g(x)−g′(x)f(x)/g(x)2 method... And it is kind of ambiguous about what would be considered the most correct simplified form with these kind of complex equations.

Either the exercise results should match the video that is referenced, the exercise should somehow clarify the specific method of final simplification format they want with these complex equations, or the input should allow the user to enter any of the 'simplified' results from either method and accept it as correct.

[quotient_rule.html?seed=71&problem=0](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/quotient_rule.html?seed=71&problem=0&debug)

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