Q. 1 L4.0( 2 Votes )

# Differentiate eac

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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