Differentiate each of the following from first principles:

We need to find derivative of f(x) = 1/x³

Derivative of a function f(x) from first principle is given by –

{where h is a very small positive number}

∴ derivative of f(x) = 1/x³ is given as –

Using algebra of limits –

Using a³ – b³ = (a – b)(a² + ab + b²)

We have:

As h is cancelled and by putting h = 0 we are not getting any indeterminate form so we can evaluate the limit directly.

Hence,

Derivative of f(x) = 1/x³