Finding trigonometric derivatives by first principles

Using Radians

 

If f(x) = sinx then f’(x) = cos x    

   Proof

   If f(x) = sinx  , find f’ (x)

Alternatively

 

Example

   If f(x) = sin5x  , find f’ (x)

 

 

If f(x) = cosx then f’(x) = -sin x    

 

Proof

Alternatively

 

If f(x) = tanx then f’(x) = 1/(cos² x ) =sec² x  

 

Proof