Derivative of complex function in Mathematica

Questions
1

Hello,
How can I solve in mathematica the complex function Z which have f(x), “M” and “a” are constants in the attached file?
How can I make it a little bit more “simplify”?

2

See code:

In[13]:= z[x_] = (1 - f[x]/M)^a f[x]

Out[13]= f[x] (1 - f[x]/M)^a

In[14]:= D[z[x], x]

Out[14]= -((a f[x] (1 - f[x]/M)^(-1 + a) Derivative[1][f][x])/
  M) + (1 - f[x]/M)^a Derivative[1][f][x]

In[15]:= Simplify[-((
   a f[x] (1 - f[x]/M)^(-1 + a) Derivative[1][f][x])/
   M) + (1 - f[x]/M)^a Derivative[1][f][x]]

Out[15]= ((M - (1 + a) f[x]) (1 - f[x]/M)^a Derivative[1][f][x])/(M - 
 f[x])