Question

Figure out the 35th derivative for xsinx. You have to do a few derivatives by hand to figure our a pattern and then predict the 35th one

Answer 1

so, did you do that?
y = -0cosx + xsinx
y' = sinx + xcosx
y" = 2cosx - xsinx
y⁽³⁾ = -3sinx - xcosx
y⁽⁴⁾ = -4cosx + xsinx

Now we are back to n*cosx + xsinx. Watch how the signs change with period 4, as well as placement of sin/cos.

Looks to me like
y⁽³⁵⁾ = -35sinx - xcosx

Answer 2

Thanks guys I appreciate the help.

Answer 3

Unfortunately I think you stopped one short. Should be 35sinx+xcosx.