What is tthe derivative D^21 of xsin(x)?

Answer 1

Is the problem to calculate the 21st derivative of xsin(x) at 0? Since x sinx is an even function it will be zero.

Answer 2

Your Teacher loves you, doesn't he (or she)?
Remember
f(x) = g(x)*h(x)
f'(x) = g(x)*h'(x) + g'(x)*h(x)
Now..... Do that 20 more times to get the 21'st derivative ☺

Yeah, it's a sh|tload and a half of terms, but it really isn't as bad as it seems at first glance since all of the terms will involve x, sin(x), or cos(x) and
d/dx x = 1
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)

And it will develop 'character' ☺

Doug

Answer 3

Are you serious? f '=sin(x)+xcos(x)

f'' = cos x + [cosx - x sin x]
f''' = - 2 sin x - [ sin x + x cos x]
f'''' = - 3 cos x - [ cosx - x sin x]
f''''' = 4 sin x - [ sin x - x cos x]

do you see the pattern?