Core 4

E.g. 2x + 3y^2+3x^2 y = 4x^2

Diff with respect to 'x'
 
Therefore

- 2+6y(dy/dx) + 3x^2 (dy/dx) + y(6x) = 8x
- 6y(dy/dx) + 3x^2 (dy/dx) + 6xy+ 2 = 8x
- (6y+3x^2) (dy/dx) = 8x - 2 - 6xy
-  (dy/dx) = (8x - 2 - 6xy)/(6y-3x^2) 

It is where you replace the 'y' with (dy/dx) when differentiating  

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Implicit Differentiation

E.g. 2x + 3y^2+3x^2 y = 4x^2

Diff with respect to 'x'
 
Therefore

- 2+6y(dy/dx) + 3x^2 (dy/dx) + y(6x) = 8x
- 6y(dy/dx) + 3x^2 (dy/dx) + 6xy+ 2 = 8x
- (6y+3x^2) (dy/dx) = 8x - 2 - 6xy
-  (dy/dx) = (8x - 2 - 6xy)/(6y-3x^2) 

It is where you replace the 'y' with (dy/dx) when differentiating  

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