xy^3-e^3x=y^2

Question

xy^3-e^3x=y^2

bobpursley · Answer

what are you trying to do?

Barbara · Answer

I am trying to find the derivative

Damon · Answer

and do you mean x y^3 - e^(3x) = y^2 ????

Barbara · Answer

yes

Damon · Answer

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?

Barbara · Answer

I have the rest but where did y^3 come from?

Damon · Answer

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

Barbara · Answer

Ooo Okay and then after don't you bring all the (dy/dx) to one side of the equation.

Barbara · Answer

After wouldn't it be x+y^3-3e^(3x)=2y(dy/dx)-3y^2(dy/dx)?

Damon · Answer

I guess. You have the idea. Now factor dy/dx out and divide I am not going to do the whole thing.

Barbara · Answer

Okay Thank You I think I got the answer

drwls · Answer

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.