It is well-known that a functions always written as ** y = f(x)**, where

**is dependent variable and**

*y***is independent variable. Those functions are known as**

*x**Some example are –*

**Explicit Functions.** **y = x ^{2} ; y = sin(x); y= ln(x); y = x^{5}+ 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)** ,

**These type of function is known as**

*sin(x) = x*^{2}+ 2xy + y^{3}.

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

Affiliated