Need help with Implicit differentiation

[EETman]

So im stuck on one problem from my homework, teacher says not to use the quotient rule because it will drag out so he says to simplify first, having trouble getting this one started.


y²=(x²/xy-4)

i can see right away that one x could be cancelled, but that doesnt remove the need to use the quotient rule.

using the quotient rule i get (x(xy-8))/(x³+2x²y³-16x²+32y), but this answer seems highly convoluted given the original function.... thanks.

 

[Deleted member 4993]

So im stuck on one problem from my homework, teacher says not to use the quotient rule because it will drag out so he says to simplify first, having trouble getting this one started.


y²=(x²/xy-4)

i can see right away that one x could be cancelled, but that doesnt remove the need to use the quotient rule.

using the quotient rule i get (x(xy-8))/(x³+2x²y³-16x²+32y), but this answer seems highly convoluted given the original function.... thanks.

Is your equation:

\(\displaystyle \displaystyle y^2 \ = \ \dfrac{x^2}{xy} \ - \ 4\) ............ this is what you wrote

or

\(\displaystyle \displaystyle y^2 \ = \ \dfrac{x^2}{xy \ - \ 4}\) ............ this is what I suspect the problem is and should have been written as y² = x²/(xy-4)

 

[HallsofIvy]

IF \(\displaystyle \dfrac{x^2}{xy}- 4= y^2\) was what you intended, then you can cancel an "x" leaving \(\displaystyle \dfrac{x}{y}- 4= y^2\).

If, as seems more likely, the problem is \(\displaystyle \dfrac{x^2}{xy- 4}= y^2\) then you cannot cancel.

In either case you will have to use the "quotient rule". What do you get?