Q. 33.7( 8 Votes )

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

3x^{2} + 2x – 5

Answer :

Let f(x) = 3x^{2} + 2x – 5

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

We know that,

…(i)

f(x) = 3x^{2} + 2x – 5

f(x + h) = 3(x + h)^{2} + 2(x + h) – 5

= 3(x^{2} + h^{2} + 2xh) + 2x + 2h – 5

[∵(a + b)^{2} = a^{2} + b^{2} + 2ab]

= 3x^{2} + 3h^{2} + 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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