Find the derivatives of the following functions at the indicated points :

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

{where h is a very small positive number}

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

{∵ sin (π + x) = – sin x & sin π = 0}

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

We need to use sandwich theorem to evaluate the limit.

Multiplying 2 in numerator and denominator to apply the formula.

⇒ f’(π/2) = –

Use the formula:

∴ f’(π/2) = – 2×1 = – 2

Hence,

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