Derivatives of Implicit Functions

It is well-known that a functions always written as y = f(x), where y is dependent variable and x is independent variable. Those functions are known as Explicit Functions. Some example are –

y = x 2 ;  y = sin(x);  y= ln(x);     y = x5+ 3x 2 + 4 x+ 10.

But, in some cases the dependent variable can not be expressed explicitly by the independent variable, like as   y = sin(xy)sin(x) = x2 + 2xy + y3. These type of function is known as  Implicit Function. 

In this part we will discuss the derivatives of implicit functions.


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