Question

What is the 1000th derivative of y=e^x(sinx)?

Answer 1

Which of the following is the question? A or B?
\[
\begin{align*}
\text{A.}\quad &y=e^{x(\sin(x))}\\
\text{B.}\quad &y=\sin(x)e^x
\end{align*}
\]

Answer 2

its B, sorry

Answer 3

i think i got the pattern going

Answer 4

let me type out what i have

Answer 5

y'= (e^x)(sinx+cosx)
y''=2(e^x)(cosx)
y'''=2(e^x)(cosx-sinx)
y''''= (-2^2)(e^x)(sinx)

Answer 6

\[y^{1000} =2y ^{999} -2y ^{998}\]

Answer 7

\[(-1)^{250} 2^{500} e^x \sin
(x)
\]
In general if k=4m, the kth derivative is
\[
(-1)^m 2^{2 m} e^x \sin (x)
\]

Answer 8

Astonishing! @eliassaab

Answer 9

the answer is (2^500)(e^x)(sinx), but idk how they got it