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)
MM
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