# Derivative - Algebra of Derivative of Functions

#### 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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