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Derivative - Algebra of Derivative of Functions

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theorem

Theorem :  Let f and g be two functions such that their derivatives are defined in a common domain. Then

(i) Derivative of sum of two functions is sum of the derivatives of the functions. 
`d/(dx)`[f(x) + g(x)] = `d/(dx)` f(x) + `d/(dx)`

(ii) Derivative of difference of two functions is difference of the derivatives of the functions. 
`d/(dx)` [ f(x) - g(x)] = `d/(dx)` f(x) - `d/(dx)` g(x).

(iii) Derivative of product of two functions is given by the following product rule. 
`d/(dx)`[f(x) . g(x)] = `d/(dx)` f(x) . g(x) + f(x) .`d/(dx)` g(x)

(iv) Derivative of quotient of two functions is given by the following quotient rule (whenever the denominator is non–zero).
`d/(dx)(f(x)/g(x))` =`[d/(dx) f(x) . g(x) - f(x) d/(dx) g(x)]/((g(x))^2)`

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