Q. 1 K5.0( 1 Vote )

# Differentiate each of the following from first principles:(x + 2)3

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

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) = (x + 2)3 is given as –

f’(x) = f’(x) = Using a3 – b3 = (a – b)(a2 + ab + b2)

f’(x) = 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) = (x + 0 + 2)2 + (x + 2)(x + 2) + (x + 2)2

f’(x) = 3 (x + 2)2

f’(x) = 3 (x + 2)2

Hence,

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

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