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

Question

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

unklerhaukus · Answer

simply*

akshay_budhkar · Answer

Ew taking derivative 6 times sounds creepy!

unklerhaukus · Answer

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

unklerhaukus · Answer

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

akshay_budhkar · Answer

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?

unklerhaukus · Answer

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