Differentiate each of the following from first principles:

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

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/√x is given as –

Using algebra of limits –

Multiplying numerator and denominator by √x + √(x + h) to rationalise the expression so that we don’t get any indeterminate form after putting value of h

Using (a + b)(a – b) = a² – b²

Using algebra of limits –

Hence,

Derivative of f(x) = 1/√x