Q. 1 H4.0( 2 Votes )

Differentiate eac

Answer :

We need to find the derivative of f(x) = kxn


Derivative of a function f(x) from first principle is given by –


{where h is a very small positive number}


derivative of f(x) = kxn is given as –





Using binomial expansion we have –


(x + h)n = nC0 xn + nC1 xn – 1h + nC2 xn – 2h2 + …… + nCn hn




Take h common –




As there is no more indeterminate, so put value of h to get the limit.



f’(x) = k nC1 xn – 1 = k nxn – 1


Hence,


Derivative of f(x) = kxn is k nxn – 1


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