Question

\[D^6(x^3e^{ax})\]
is there way to solve this problem that is simpler than taking the derivative 6 times

Answer 1

simply*

Answer 2

Ew taking derivative 6 times sounds creepy!

Answer 3

yeah i got to the righ answer, after many hours of work

Answer 4

but 13 lines is so many for such a simple looking question

is there some way to solve it as a sixth order product or someting

Answer 5

i will go for differentiating it 6 times o_O? I don't think we can skip and differential by using some trick can we?

Answer 6

the answer
\[(120+90ax+18a^2x^2+a^3x^3)a^3e^{ax}\]

has numbers that kinda look like numbers you might find in the pascal triangle thing