Question

Differentiate each of the following from first principles:

1/x³

Answer 1

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 –

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