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[tex]\frac{2x+y}{x-3y}=4[/tex]

Now, if you just solve it as is, using implicit differentiation, you get the deriviative to be y/x.

However, if you multiply by the denominator, you get...

[tex]2x+y = 4(x-3y)[/tex]

...or...

[tex]2x+y=4x-12y[/tex]

...and if you do implicit differentiation, you get the deriviate to be 2/13.

Why are there two solutions like that, and is any of the two any more right than the other?

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# 2 totally different answers?

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