Alternatively, you can use the positional derivative package (pdiff).
(%i1) load(pdiff)$
Here g[(n)] is the n-th derivative of g (a function of one variable).
(%i2) diff(f(g(x)),x);
(%o2) g[(1)](x)*f[(1)](g(x))
(%i3) diff(f(g(x)),x,2);
(%o3) g[(1)](x)^2*f[(2)](g(x))+g[(2)](x)*f[(1)](g(x))
And f[(m,n)] is the m-the derivative with respect to the first variable
and the n-the derivative with respect to the second:
(%i4) diff(f(x,y),y);
(%o4) f[(0,1)](x,y)
(%i6) diff(f(x,x^2),x);
(%o6) f[(1,0)](x,x^2)+2*x*f[(0,1)](x,x^2)
--Barton