Q. 1 L4.0( 2 Votes )

Differentiate each of the following from first principles:

x3 + 4x2 + 3x + 2

Answer :

We need to find the derivative of f(x) = x3 + 4x2 + 3x + 2


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


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


derivative of f(x) = x3 + 4x2 + 3x + 2is given as –


f’(x) =


f’(x) =


f’(x) =


Using (a + b)2 = a2 + 2ab + b2 , we have –


f’(x) =


f’(x) =


f’(x) =


Take h common –


f’(x) =


As h is cancelled, so there is no more indeterminate form possible if we put value of h = 0.


So, evaluate the limit by putting h = 0


f’(x) =


f’(x) = 3x2 + 3x(0) + 8x + 3 + 02 + 4(0)


f’(x) = 3x2 + 8x + 3


Hence,


Derivative of f(x) = x3 + 4x2 + 3x + 2 is 3x2 + 8x + 3


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