Differentiate the following functions with respect to x :

$c o s (x + a)$

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Solution

We have,

$\frac{d}{d x} {c o s (x + a)}$

$= \frac{d}{d x} {c o s x . c o s a - s i n x . s i n a}$

$[∵ c o s (x + a) = c o s x c o s a - s i n x s i n a]$

$= c o s a \frac{d}{d x} (c o s x) - s i n a - \frac{d}{d x} (s i n x)$

$= c o s a (- s i n x) - s i n a (c o s x)$

$= c o s x s i n a + s i n x + c o s a$

$= - (s i n x c o s a + c o s x s i n a)$

$= - s i n (x + a)$

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