How to Derive Using the Chain Rule for 2x^2+5xy-y^2=1?

lemonlee
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Homework Statement


2x^2+5xy-y^2=1


Homework Equations


d/dx(f(u)x))=df/du * du/dx


The Attempt at a Solution



i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?
 
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lemonlee said:
i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?

Assuming that you are trying to find \frac{dy}{dx} (you didn't actually tell us what you are trying to calculate!), then it is wrong...However, I can't tell you what you did wrong since you haven't shown me what you did to get your answer...if you do that, I'll be able to help you :wink:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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