Differentiate the following with respect to x:

cos (x + a)

Given,

f(x) = cos (x + a)

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

∴ f(x) = cos x cos a – sin x sin a

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) = – sin x cos a – sin a cos x

⇒ f’(x) = – (sin x cos a + sin a cos x)

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

∴ f’(x) = – sin (x + a)