Q. 33.7( 8 Votes )

Find the derivation of each of the following from the first principle:

3x2 + 2x – 5

Answer :

Let f(x) = 3x2 + 2x – 5

We need to find the derivative of f(x) i.e. f’(x)


We know that,


…(i)


f(x) = 3x2 + 2x – 5


f(x + h) = 3(x + h)2 + 2(x + h) – 5


= 3(x2 + h2 + 2xh) + 2x + 2h – 5


[(a + b)2 = a2 + b2 + 2ab]


= 3x2 + 3h2 + 6xh + 2x + 2h – 5


Putting values in (i), we get






Putting h = 0, we get


f’(x) = 3(0) + 6x + 2


= 6x + 2


Hence, f’(x) = 6x + 2


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