- #1
Inspector Gadget
- 31
- 0
This was given as a problem...
[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?
[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?