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

Question

Find the derivation of each of the following from the first principle: 3x 2 + 2x – 5

Philoid · Accepted 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