Derivative

Derivative The functional derivatives represents a minute modification in the function with respect to one of its variables. The simple derivative of a function f with respect to a variable x is denoted either f(x) or (df)/(dx).(1) It is often written in-line as df/dx. When derivatives are taken relating to time, they are being denoted using Newtons overdot (A single dot above x) note for fluxions, (dx)/(dt)=x^.. ..(2) When any derivatives are taken n times, the notation f^(n) (x) or we can represent as: (d^nf)/(dx^n) .(3) There are some important rules for computing derivatives of definite combinations of functions. Derivatives of sums are exactly equal to the sum of derivatives, so that [f (x)+..+h(x)] = f (x)+..+h (x) f(x) is the derivative of f(x) which is defined as Example 1: Find the derivative of f(x) = x -8x +12. Find the derivative by using the definition of derivative. Answer: 1st Method Formulae: ddx (xn) = n x(n-1) ddx (a) = 0, here a is constant These formulae can also be used in order to find the derivatives. Example 2: Find the derivative of f(x) = x -8x +12 Answer: 2nd method ddx (xn) = n x(n-1) ddx (x2) = 2 x2-1 = 2x ddx (-8x) = -8 ddx (x)= -8.1.x1-1 = -8 ddx (12) = 0 f(x) = 2x - 8