Rewrite a symbolic function in terms of a defined function

How can I rewrite a symbolic expression or function in terms of another defined function? Specifically, I want to rewrite df in terms of f:

syms z
f=1/(1+exp(-z))
df=diff(f)

The result should be

   f(1-f)

[Amin Yahyaabadi]

I know function subexpr, which automatically selects the common subexpression (I can not define my subexpression), and it uses exp(z).

subexpr(df)
sigma = 
  exp(-z)

ans =
   sigma/(sigma + 1)^2

, and rewrite, which uses predefined functions like sin or exp

, and has, which only says if that subexpr exist in the function!

has(df,f)
ans=
1

also the following does not work:

syms a
subs(df,1/(1+exp(-z)),a)

ans =

a^2*exp(-z)

Answer 1

[madhan ravi]

syms z
f=1/(1+exp(-z))
df=diff(f)

isolate(df==1,f)

[madhan ravi]

see isolate() it maybe the one you are looking for

[madhan ravi]

if something is not clear let know with an example to get a clear picture

[Amin Yahyaabadi]

It does not what I want. There is no equation in my case! Maybe, I can write an equation to do this for me indirectly, but it does not give f(1-f) directly.

[madhan ravi]

As far as I know ,I don't think there is a command to do that