Math in Biometrics

Mathematical Analysis

Leibniz's Notation
Who is Leibniz 
 Gottfried Wilhelm Leibniz (1646 - 1716) was a 17th century German mathematician. He’s often credited with developing many of the main principles of differential and integral calculus, and is primarily recognized for what we now call Leibniz’s notation. 
 
 
 
 
 Leibniz's Notation System 
 The derivative of a function based on today’s standard is given by: 
 
 
 
 
 Leibniz's notation expresses the derivative as: 
 
 
 
 where goes toward 0. 
 Fractional Behavior 
 Let’s review some examples where Leibniz’s notation is often utilized. The Chain Rule using Lagrange Notation states: 
 
 
 
 
 We can translate the above Chain Rule into Leibniz's Notation as: 
 
 
 
 
 In the above equations, we can see how Leibniz’s Notation behaves similarly to a fraction, although it must be emphasized that the derivative is not a fraction. 
 Try It on a Function 
 Let us try . 
 
 Click to Expand/Collapse 
 Expand the function: 
 
 
 
 Simplify fraction: 
 
 
 
 
 
 So the derivative of is .