derivative of sin(sin(sinx))

derivative of sin(sin(sinx)), example of chain rule, how to solve a chain rule problem?, solve the derivative using the chain rule 

derivative of sin(sin(sin x))

use formula of chain rule 

                                      =>d/dx (sin y) = cos y * dy/dx

               the value of y= sin (sin x) 

use above formula we get  
                                    => cos (sin (sinx))*d/dx (sin(sin x))

    now new value of  y = sinx 

use above formula again we get 
                                     => cos (sin (sin x))* cos(sin x) * d/dx sin x 

now use the same formula again we get 
                                     => cos (sin (sin x))* cos(sin x) * cos x 

Answer =  cos (sin (sin x))* cos(sin x) * cos x