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

{where h is a very small positive number}

∴ derivative of 2cos x at x = π/2 is given as –

{∵ cos (π/2 + x) = – sin x }

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

⇒ f’(π/2) =

Use the formula:

∴ f’(π/2) = – 2×1 = – 2

Hence,

Derivative of f(x) = 2cos x at x = π/2 is – 2