Explicit equations
Explicit equations are the type we are most familiar with eg y=f(x), y = 2x² + 3x - 5 etc. where y is expressed in terms of x or some other variable.
Implicit equations
Implicit equations have the structure of being a mix of x and y terms eg 2x²+ 3xy - 3y² = 5 , so y cannot be expressed in terms of x.
The method for solving equations of this type is to regard the whole expression as a function of x and to differentiate both sides of the equation. Any power of y is treated as a 'function of a function', as y is a function of x.

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Example #1

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Example #2

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Example #3