Differentiation of Trigonometric Functions

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