kill(all);

van=facebook.com/LearningCalculus$

f(x):=e^x*x^n$

max:1;

A: create_list(diff(f(x),x,k),k,max,max);

factor(A);

subst(a,e^x,A);

subst(b,log(e),%);

factor(%);

fullratsimp(b^4*x^4+4*b^3*n*x^3+6*b^2*n^2*x^2-6*b^2*n*x^2+4*b*n^3*x-12*b*n^2*x+8*b*n*x+n^4-6*n^3+11*n^2-6*n);

vec:[1,4,6,-6,4];

sum(b^i*n^(max-i)*x^i*max,i,1,max);

create_list(expand(binomial(i*x,2)),i,1,6);

create_list(expand(binomial(i*x,3)),i,1,6);

create_list(nterms(%[i]), i, 1, length(%));

create_list(expand(binomial(sin(i*%pi*x),2)),i,1,6);

expand(binomial(x,3));

expand(binomial(binomial(binomial(b,n),x),2));

Ac: create_list(nterms(A[i]), i, 1, length(A));

diff(f(x),x,1);

sum(e^x*log(e)^i+sum(e^x*log(e)^j,j,1,i),i,1,4);

nthderivative(i):=(-1)^(n)*2*n!/x^(n+1);

B: create_list(nthderivative(n),n,1,6);

fullratsimp(nthderivative(i));

is(equal(A,B));