calculus and analysis - Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$? We have to use a conditional or pattern test so that the function accepts any symbols as input except for lists.

I will show all my attempts and I have some questions about why certain ways are wrong and why are they wrong. I am new to Mathematica and still not very familiar about how it works.

Here are all my attempts:

1).
In: $f = x^{2};$
In: func[f_] = $\frac{1}{f} f'$
Out: $\frac{(x^{2})'}{x^{2}}$
This attempt is wrong because first we are not using conditional or pattern test. Also, why cannot we differentiate the function by using the ' sign?

2).
In: $f = x^{2};$
In: func[f_] := $\frac{1}{f} f'$
Out: No output
Why is there no output when I use delayed assignment?

3).
In: $f = x^{2};$
In: func[f_,x_] = $\frac{1}{f} f'$
Out: $\frac{(x^{2})'}{x^{2}}$
Is adding another argument x_ redundant, or does it make any difference?

4).
In: $f = x^{2};$
In: func[f_] = Module[{f}, Switch[f, _Symbol, $\frac{1}{f} f'$]] Output: $\frac{f$8344'}{f$8344}$
The syntax might not make any sense, but I am struggling to find ways to fix it. And I might have used _Symbol incorrectly, what is _Symbol after all?

Now I am trying to write the function in a less general way.

5).
Now In: $f = x^{2};$
In: func[f_] = $\frac{1}{f} D[f,x]$
Output: $\frac{2}{x}$
This method of course works but if I change the input to f = $y^{2}$, the function will return 0 as output.
One way to solve this is by changing to func[f_] = $\frac{1}{f} D[f,y]$, but I think this is considered as cheating, since we are not really answering the question and meeting the requirements set by the question.

What really makes me struggle is to compute the derivative, how can we compute the derivative of the input function with respect to its independent variable.

Also, I don't fully understand the Switch condition:
It is mentioned in Mathematica Help, that Switch evaluates $expr_i$, then compares it with each of the $form_i$ in turn, evaluating and returning the $value_i$. What is form and what is value?
Suppose I write the function:

In: f[x_] := Switch[x, x>0, 1, x<=0, 0] In: {f[5], f[-5], f[x]}
Out: {0,0,0}
Am I using the wrong form?

Any detailed help is greatly appreciated. Thanks!

Answer

Here's another way to proceed, using Derivative[], and sidestepping the use of a dummy variable:

LogDerivative[f_] := Derivative[1][Composition[Log, f]]

Test:

LogDerivative[Sin][x]

   Cot[x]

LogDerivative[Gamma][x]
   PolyGamma[0, x]

LogDerivative[#^3 &][x]
   3/x