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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 Newton's 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)

f¹(x) is the derivative of f(x) which is defined as

(df)/(dx)…….(1)

It is often written in-line as df/dx. When derivatives are taken relating to time, they are being denoted using Newton's 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)

f¹(x) is the derivative of f(x) which is defined as

Formulae:

These formulae can also be used in order to find the derivatives.

f¹(x) = 2x - 8