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Motion In A Straight Line

Differentiation

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 $\frac{1}{x}$ 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

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

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