Given,

f(x) =

Using cos (A + B) = cos A cos B – sin A sin B, we get –

∴ f(x) =

⇒ f(x) = cos 2 cot x – sin 2

we need to find f’(x), so differentiating both sides with respect to x –

∴ )

Using algebra of derivatives –

⇒ f’(x) =

As cos a and sin a are constants, so using algebra of derivatives we have –

⇒ f’(x) =

Use the formula:

∴ f’(x) = – cosec² x cos 2 – sin 2 (0)

⇒ f’(x) = – cosec² x cos 2 – 0

∴ f’(x) = – cosec² x cos 2