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Basic Mathematics(Pre-requisite)


Differentiation is the process of obtaining the derived function f′(x) from the function f(x), where f′(x) is the derivative of f at x.

The derivatives of certain common functions are given in the Table of derivatives,

Table of derivatives :

f(x) f'(x)
xn nxn-1
sin x cos x
cos x -sin x
tan x sec2 x
cot x -cosec2 x
sec x sec x tan x
cosec x -(cosec x )(cot x)
ln x 1x
ex ex

Many other functions can be differentiated using the following rules of differentiation:

(i) If h(x) = k f(x) for all x, where k is a constant, then h′(x) = k f′(x).

(ii) If h(x) = f(x) + g(x) for all x, then h′ (x) = f′(x) + g′(x).

(iii) The product rule: If h(x) = f(x)g(x) for all x, then h′(x) = f(x)g′(x) + f′(x)+g′(x).

(iv) The reciprocal rule: If h(x) = 1/f(x) and f(x) ≠ 0 for all x, then

h'(x) = -f'(x)(f(x))2

(v) The quotient rule: If h(x) = f(x)/g(x) and g(x) ≠ 0 for all x, then

h'(x) = g(x)f'(x)-f(x)g'(x)(g(x))2

(vi) The chain rule: If h(x) = (g)(x) = f(g(x)) for all x, then h′(x) = f′(g(x))g′(x).


Integration is the process of findin…

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