Derivatives of Unknown Functions

Differentiating a known function gives an explicit result:

D[Log[x]^2,x]

Differentiating an unknown function f gives a result in terms of f':

D[f[x]^2,x]

The Wolfram Language applies the chain rule for differentiation, and leaves the result in terms of f':

D[x f[x^2],x]

Differentiating again gives a result in terms of f, f', and f'':

D[%,x]

When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated:

D[g[x^2,y^2],x]

This represents (∂/(∂x))(∂/(∂x))(∂/(∂y))g(x,y). The Wolfram Language assumes that the order in which derivatives are taken with respect to different variables is irrelevant:

D[g[x,y],x,x,y]

You can find the value of the derivative when x==0 by replacing x with 0:

%/.x->0

Output forms for derivatives of unknown functions.