Find the derivative of f(x) = tan x at x = 0

Derivative of a function f(x) at any real number a is given by –

{where h is a very small positive number}

∴ derivative of cos x at x = 0 is given as –

∵ we can’t find the limit by direct substitution as it gives 0/0 (indeterminate form)

∴ Use the formula: {sandwich theorem}

∴ f’(0) = 1

Hence,

Derivative of f(x) = tan x at x = 0 is 1