Till now, the functions that we have discussed, are explicitly functions of x. We have defined y in terms of x. Suppose we have an equation f(x,y) = 0, which cannot be put in the form of y=f(x) to differentiate in the usual way, we can still differentiate the equation f(x,y) = 0. This function in which y cannot be expressed in terms of x, is called an implicit function.Till now, the functions that we have discussed, are explicitly functions of x. We have defined y in terms of x. Suppose we have an equation f(x,y) = 0, which cannot be put in the form of y=f(x) to differentiate in the usual way, we can still differentiate the equation f(x,y) = 0. This function in which y cannot be expressed in terms of x, is called an implicit function.
x3+ y3- 9xy = 0 is an example of an implicit function.
The process of differentiating implicit function is called implicit differentiation.
Rules for Implicit Differentiation
Step 1:
Step 2:
Differentiate the terms containing x, y or both xy with respect to x.
While differentiating the terms containing y or power of y, first 
Step 3:
Step 4:
Example:
Differentiate the following implicit equation
ax
2 + 2hxy + by
2 + 2gx + 2fy + c = 0
Step 1:
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
Step 2:
Differentiating with respect to x, we have
Step 3:
Step 4:
