Q:

A good differentiation problem

Could anyone please help with the simplification? or highlight short tricks, if any? It'd be great help. Thanks a lot. 

A:

$$\frac{1}{y}'=-\frac{1}{y^2}y'$$
For rest, further diffrenciate it to get 
$$\frac{1}{y}''=-\frac{1}{y^2}y''+(\frac{2}{y^3})y'$$
and so on..

