Limits and Derivatives

Limits and Derivatives

Question

For some constants a and b, find the derivatives of the following functions :

(x-a)(x-b)

Answer

Let       space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight y space equals space left parenthesis straight x minus straight a right parenthesis left parenthesis straight x minus straight b right parenthesis equals straight x squared space minus ax minus 0 bx plus ab
rightwards double arrow                             y = x2 - (a+b)x + ab

∴     space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space dx over dx equals straight d over dx straight x squared minus straight d over dx left parenthesis straight a plus straight b right parenthesis straight x plus straight d over dx left parenthesis ab right parenthesis equals 2 straight x minus left parenthesis straight a plus straight b right parenthesis straight d over dx straight x plus 0
                                 = 2x-(a+b).1=2x-(a+b)

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