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3.5.3 Derivatives of Unknown Functions
Differentiating a known function gives an explicit result.
In:= D[Log[x]^2, x]
Differentiating an unknown function f gives a result in terms of f'.
In:= D[f[x]^2, x]
Mathematica applies the chain rule for differentiation, and leaves the result in terms of f'.
In:= D[x f[x^2], x]
Differentiating again gives a result in terms of f, f' and f''.
In:= D[%, x]
When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.
In:= D[g[x^2, y^2], x]
This represents . Mathematica assumes that the order in which derivatives are taken with respect to different variables is irrelevant.
In:= D[g[x, y], x, x, y]
You can find the value of the derivative when by replacing x with 0.
In:= % /. x->0
Output forms for derivatives of unknown functions.