Well, I did not find out how to do the assignment of a function to a letter (e.g. f(x) = sin(x)) work with the single command line in Wolframalpha - except for the very simple case shown above. So I found an old Maxima release that I had on an old CD from university times. There the calculation worked out fine.

Hello Dent de Lion,

very funny and curious answers that you got from Wolframalpha. ;-)

In fact I tried all your suggested notations like "/. {f -> sin(x)}", "D[f, x]" and they always work with the easy formula, like the derivative of sin(x) alone. But when you add "+1" to the expression which shall be derived, then the interpretation goes wrong or the programme writes down sin'(x) or sin(x)' but does not evaluate it to cos(x). Why not? It seems to understand that it should now compute the derivative of sin(x) but it does NOT do it. Very strange, because if you do the derivative directly e.g. "d (sin(x)+1)/dx" it does it, even for very complicated input. This should do with substituting the complex input as f, too.

Therefore my question: Why does the substitution of f with the command "where" sometimes work and with a small variation it does not work anymore.

it's all about input interpretation, of course: The program (Mathematica) has a free language input (the orange equal sign), working with it one gets

as you see, the input interpretation is correct in $\LaTeX$, but not in Mathematica, it must be

In[18]:= 1 + Derivative[1][f][x] /. {f -> Sin}
Out[18]= 1 + Cos[x]

Two other interpretations missing the point are

to be honest I was inapt to get the result out of the free language input with Mathematica 10.1 within half an hour.

In[8]:= ?Where

During evaluation of In[8]:= Information::notfound: Symbol Where not found. >>

In[9]:= f[x_] := Sin[x]

In[10]:= 2 f[x] + Sin[x]^2

Out[10]= 2 Sin[x] + Sin[x]^2

In[11]:= f'[x] + 1

Out[11]= 1 + Cos[x]