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)