It is possible to find the derivative of trigonometric functions.

Here is a list of the derivatives that you need to know:

d (sin x)  =  cos x
dx

d (cos x)  = –sin x
dx

d (sec x)   =  sec x tan x
dx

d (cosec x) = –cosec x cot x
dx

d (tan x) =  sec²x
dx

d (cot x)  =  –cosec²x
dx

One condition upon these results is that x must be measured in radians.

Applying the Chain Rule

The chain rule is used to differentiate harder trigonometric functions.

Example

Differentiate cos³x with respect to x.
Let y = cos³x
Let u = cos x
therefore y = u³
dy   =  3u²
du

du  =  -sin x
dx

dy  =  du  ×  dy
dx      dx       du
     =  -sin x × 3u²
     = -sin x × 3cos²x
= -3cos²x sin x