>>286
(d/dx)^n log (1-x)
= (d/dx)^{n-1} -1/(1-x)
= -(n-1)!/(1-x)^n

(d/dx)^n exp(x) cos(x)
= (d/dx)^n Re[ exp((1+i)x) ]
= Re[ (1+i)^n exp((1+i)x) ]
= 2^{n/2} Re[ exp((nπ/4 + x)i + x) ]
= 2^{n/2} exp(x) cos(nπ/4 + x)

(d/dx)^n x^3 sin(x)
= lim[a→1] (d/dx)^n x^3 sin(ax)
(d/dx)^n x^3 sin(ax)
= (d/dx)^n (d/da)^3 cos(ax)
= (d/da)^3 (d/dx)^n cos(ax)
= (d/da)^3 Re [ i^n a^n exp(iax) ]
= (d/da)^3 a^n Re [ exp((nπ/2 + ax)i) ]
= (d/da)^3 a^n cos(nπ/2 + ax)
→ n(n-1)(n-2) cos(nπ/2 + x) - 3 n(n-1) x sin(nπ/2 + x) - 3 n cos(nπ/2 + x) + sin(nπ/2 + x)