Differentiate each of the following from first principles: (x^2 + 1)/x

Question

Differentiate each of the following from first principles:

\(\frac{x^2+1}{x}\)

Answer 1

We need to find derivative of \(\text{f(x)}=\frac{x^2+1}{x}\)

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

{where h is a very small positive number}

Using algebra of limits –

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