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}