Example   determines the first four derivatives for following.

                                                                 y = cos x

Solution: Again, let's just do some derivatives.

y = cos x

y′ = - sin x

 y′′ = - cos x

y′′′ = sin x

y^{( 4)}  = cos x

Note as well that cosine (and sine) will repeat each four derivatives. The other four trig functions will not demonstrate this behavior. You may desire to take a few derivatives to convince yourself of this.