Differentiate the following from first principle.
(–x) – 1
We need to find derivative of f(x) = ( – x) – 1 = – 1/x
Derivative of a function f(x) is given by –
f’(x) = {where h is a very small positive number}
∴ derivative of f(x) = – 1/x is given as –
f’(x) =
⇒ f’(x) =
⇒ f’(x) =
⇒ f’(x) =
As h is cancelled and by putting h = 0 we are not getting any indeterminate form so we can evaluate the limit directly.
∴ f’(x) =
Hence,
Derivative of f(x) = ( – x) – 1