Question

Differentiate the following from first principles

tan x²

Answer 1

We need to find derivative of f(x) = tan x²

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

{where h is a very small positive number}

∴ derivative of f(x) = tan x² is given as –

Use the formula: sin (A – B) = sin A cos B – cos A sin B

∴ To use the sandwich theorem to evaluate the limit, we need 2hx + h² in denominator. So multiplying this in numerator and denominator.