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