Pensieve header: Experimenting with changing the dependent and independent variables.

f'[x] // FullForm

f''[x] // FullForm

f'[x]/.f->(f[g[#]]&)

f''[x]/.f->(f[g[#]]&)

f'[x] /. f -> (f[#]g[#]&)

f''[x] /. f -> (f[#]g[#]&)