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