Find dy/dx from the equation 2xy + 3x^2 = 4y

Firstly we must notice that we can differentiate each term separately.

Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and v=y and using (uv)'= uv' + vu' we get the term 2y+2xy'.

For the 3x^2 term, we can differentiate as usual to get 6x.

For the 4y term, we can simply differentiate to get 4y'.

Putting this all together we get: 2y+2xy'+6x=4y'.

Finally, rearranging gives dy/dx=(3x+y)/(2-x)