How to compute the sensitivity of this control system?
Start with the two expressions: 

$$T=\frac{G_c G }{1+ H G_c G}, \ \ \ \ \ \ \ \ \ \ \ \ S_G^T=\frac{\partial T}{\partial G}\frac{G}{T} $$

Compute the first term: 

$$ \frac{\partial T}{\partial G} = \frac{G_c }{1+H G_c G}- \frac{H G_c^2 G }{(1+HG_c G)^2}= \frac{G_c+H G_c^2 G-H G_c^2 G }{(1+H G_c G)^2}=\frac{G_c }{(1+H G_c G)^2}$$

And substitute values to get the final expression:

$$ S_G^T= \frac{G_c }{(1+H G_c G)^2}\frac{G}{\frac{G_c G }{1+ H G_c G}} = \frac{1}{1+H G_c G}$$