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