Differentiate each of the following from first principles:
We need to find derivative of f(x) =
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) = is given as –
f’(x) =
⇒ f’(x) =
⇒ f’(x) =
⇒ f’(x) =
Using algebra of limits –
⇒ f’(x) =
⇒ f’(x) =
⇒ f’(x) =
⇒ f’(x) =
⇒ f’(x) =
∴ f’(x) =
Hence,
Derivative of f(x) =