I. Concepts and formulae:
1) Let f(x) be a function in x. Let it be denoted as y = f(x) where 'x' is an independent variable and 'y', a dependent variable.
         Let x be a small change in 'x'. Correspondingly, let y be the small change in 'y'. Therefore, we have

2) The other notation which is in common use is as follows:
       f'(x) =    where 'h' is a small change in 'x'.
3) The derivative of a function at x = a is defined as
       f'(a) =  
4) For x  R, f(x) =  is not differentiable at zero and is differentiable for x ≠ 0.
5) The derivative of a constant function is zero.
6) If f(x) is differentiable at x = a, then f(x) is continuous at x = a. The converse of this need not be true.
7) Some of the standard derivatives are given below:

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