Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (2x, 0)

given function is

                                                   $y=\sin \left(\sin x\right)$

tangent at point $\left(2\mathrm{\pi }, 0\right)$

derivative of the function,

                                                  $\begin{array}{rcl}\frac{d}{dx}y& =& \frac{d}{dx}\sin \left(\sin x\right)\\ \frac{dy}{dx}& =& \frac{d\sin \left(\sin x\right)}{d\sin x}\frac{d\sin x}{dx}\\ & =& \cos \left(\sin x\right)\cos x\end{array}$

slope of tangent line will be value of derivative at the point, so

                                                      $\begin{array}{rcl}m& =& {\left(\frac{dy}{dx}\right)}_{x=2\mathrm{\pi }}\\ m& =& \cos \left(\sin 2\mathrm{\pi }\right)\cos 2\mathrm{\pi }\\ & =& \cos 0\\ \mathrm{m}& =& 1\end{array}$