Q. 2 B4.5( 2 Votes )

Differentiate the

Answer :

We need to find derivative of f(x) = e3x


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


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


derivative of f(x) = e3x is given as –


f’(x) =


f’(x) =


f’(x) =


Taking e – x common, we have –


f’(x) =


Using algebra of limits –


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.


f’(x) =


Use the formula:


f’(x) = e3x × (3)


f’(x) = 3e3x


Hence,


Derivative of f(x) = e3x = 3e3x


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