Differentiate each of the following from first principles:

x2 + x + 3

We need to find the derivative of f(x) = x2 + x + 3


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


{where h is a very small positive number}


derivative of f(x) = x2 + x + 3 is given as –


f’(x) =


f’(x) =


Using (a + b)2 = a2 + 2ab + b2


f’(x) =


f’(x) =


Take h common –


f’(x) =


f’(x) =


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


f’(x) = (2x + 0 + 1)


f’(x) = 2x + 1 = 2x + 1


Hence,


Derivative of f(x) = x2 + x + 3 is (2x + 1)


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