Differentiation

Important Note:
The symbol dy/dx is used for the derivatives of y with respect to x and here it is not a quotient of dy and dx. dy/dx is also denoted by y'.

Differentiation By Definition or By Ab-initio or From First Principles:
Following four steps involve in finding the derivative of f(x):

• Step-I: Find f(x + δx)
• Step-II: Simplify f(x + δx) - f(x)
• Step-III: Divide f(x + δx) - f(x) by δx to get [f(x + δx) - f(x)] ∕ δx
• Step-IV: Find lim δx→0 [f(x + δx) - f(x)] ∕ δx

The method of finding derivatives by this process is called differentiation by definition or by ab-initio or from first principles.