Q. 3 L5.0( 2 Votes )

Differentiate the

Answer :

We need to find derivative of f(x) =


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


f’(x) = {where h is a very small positive number}


derivative of f(x) = is given as –


f’(x) =


f’(x) =


f’(x) =


Taking common, we have –


f’(x) =


Using algebra of limits –


f’(x) =


f’(x) =


As one of the limits can’t be evaluated by directly putting the value of h as it will take 0/0 form.


So we need to take steps to find its value.


As h 0 so, (2hx + h2) 0


multiplying numerator and denominator by (2hx + h2) in order to apply the formula –


f’(x) =


Again using algebra of limits, we have –


f’(x) =


Use the formula:


f’(x) =


f’(x) =


f’(x) =


Hence,


Derivative of f(x) =


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