Differentiate each of the following from first principles:
x2 + x + 3
We need to find the derivative of f(x) = x2 + x + 3
Derivative of a function f(x) from first principle is given by –
{where h is a very small positive number}
∴ derivative of f(x) = x2 + x + 3 is given as –
f’(x) =
⇒ f’(x) =
Using (a + b)2 = a2 + 2ab + b2
⇒ f’(x) =
⇒ f’(x) =
Take h common –
⇒ f’(x) =
⇒ f’(x) =
As there is no more indeterminate, so put value of h to get the limit.
⇒ f’(x) = (2x + 0 + 1)
⇒ f’(x) = 2x + 1 = 2x + 1
Hence,
Derivative of f(x) = x2 + x + 3 is (2x + 1)