Asked by Barbara

xy^3-e^3x=y^2
Answered by bobpursley
what are you trying to do?
Answered by Barbara
I am trying to find the derivative
Answered by Damon
and do you mean
x y^3 - e^(3x) = y^2 ????
Answered by Barbara
yes
Answered by Damon
Oh
If my guess is correct
x (3 y^2) dy/dx + y^3 - 3 e^(3x) = 2 y dy/dx
does that get you started?
Answered by Barbara
I have the rest but where did y^3 come from?
Answered by Damon
d/dx (a b) = a db/dx + b da/dx
so
d/dx [ x (y^3) ] = x d(y^3)/dx) + y^3 dx/dx
Answered by Barbara
Ooo Okay and then after don't you bring all the (dy/dx) to one side of the equation.
Answered by Barbara
After wouldn't it be x+y^3-3e^(3x)=2y(dy/dx)-3y^2(dy/dx)?
Answered by Damon
I guess. You have the idea. Now factor dy/dx out and divide I am not going to do the whole thing.
Answered by Barbara
Okay Thank You I think I got the answer
Answered by drwls
There is a name for this type of problem, where you calculate dy/dx in terms of x AND y, without knowing or having to solve for y(x) first.

It is called implicit differentiation. You are on the right track with your solution.
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