Question

Find a formula for the nth derivative of
f(x) = e^(-x/3)

Answer 1

you will need a -1^n

Answer 2

(-1/3)^n . f(x)

Answer 3

\[f ^{n}(x)=(\frac{-1}{3})^ne^{\frac{-x}{3}}\]

Answer 4

Oh yeah, what he said :P

Answer 5

(-1/3)^n . f(x)...does that always work?? replacing 1/3 with whatever is in the prob..

Answer 6

no its only fr this case..

Answer 7

In general:\[f ^{n}(e^m)=m^n e^m\]

Answer 8

the general case is
\[f^{(n)}(x) = (g'(x))^{n} . f(x) \]
if
\[f(x) = e^{g(x)}\]

Answer 9

that helps alot! thanks guys

Answer 10

welcome

Answer 11

No problem.