There is a Calculus Implicit problem that i cannot seem to find the next step i have the answer i just dont seem to know how they got the positive and negative values in the answer...would anyone know how to solve it?

find dy/dx, given x^2+ xy -y^3 = 7

My work includes:

2x+y+x dy/dx -3y^2 dy/dx= 0

After this im not sure exactly how to simplify..

Question

There is a Calculus Implicit problem that i cannot seem to find the next step i have the answer i just dont seem to know how they got the positive and negative values in the answer...would anyone know how to solve it?

find dy/dx, given x^2+ xy -y^3 = 7

My work includes:

2x+y+x dy/dx -3y^2 dy/dx= 0

After this im not sure exactly how to simplify..

jim_thompson5910 · Answer

The goal is to isolate dy/dx. Think of this as one variable. If it helps, let z = dy/dx

so 
$$\Large 2x+y+x*\color{red}{\frac{dy}{dx}} -3y^2*\color{red}{\frac{dy}{dx}}= 0$$
turns into 
$$\Large 2x+y+x*\color{red}{z} -3y^2*\color{red}{z}= 0$$


solve the equation for z. When z is fully isolated, replace z with dy/dx

anonymous · Answer

Thank You so Much, that really helped.

jim_thompson5910 · Answer

I'm glad it makes much more sense now

anonymous · Answer

Yes i appreciate it