Fundamental rules for differentiation:

fundamental rules for differentiation

(i) Differentiation of the constant function = 0

            i.e.       dc/dx = 0;

(ii) Derivative of sum: Let u, v be 2 derivable functions of x so denoting their sum by y, we write, y = u + v

            so, 

(iii). Derivative of the difference: Let u, v be 2 derivable function of x, so denoting their difference by y, thus write y = u -v

            so, 

(iv). Generalisation: By a repeated application of results obtained above, it can be proved that if u₁, u₂ ......, u_n be any finite number of the derivable functions, then

            y = u₁ ± u₂ ± u₃ ± ....... ± u_n

Example: Find out .

Solution:       Let y = x + 1/x, so let u = x₁ and v = 1/x

                        So y = u + v

Example: Find out 

Solution:       Assume y = x² - 1/x, so let u = x² and v = 1/x

                        So y = u - v

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