Question

calculate the 35 derivative of x sin(piX) by calculating the first few derivatives and seeing the pattern that occurs. I have tried this question but get a really long couple of lines and cannot see a pattern which makes me think I am doing it wrong.

Answer 1

What did you get for the first four derivatives?

Answer 2

My first derivative was sin(pix) + pi x cos(pix)

Answer 3

My second derivative was pi cos(pix) - {pi sin(pix) [pi cos(pix) +pix]}

Answer 4

the spaces are multiplications

Answer 5

The third derivative is the one where i started to get really confused I could not even simplify it but I will type out the nonsimplified line if you want

Answer 6

If you want me to type it out please let me know as it is quite long and may take me a few minutes to type out

Answer 7

The 2nd derivative is not correct.

f(x) = x*sin(pi*x)
f'(x) = sin(pi*x) +pi*x*cos(pi*x)
f''(x) = pi*cos(pi*x) + pi*cos(pi*x) - pi^2*x*sin(pi*x)
= 2pi*cos(pi*x) -pi^2*x*sin(pi*x)

Answer 8

thank you I have no idea where I got the + pi*x on my work from I that should make it much easier to solve I will comment on this question again if I need more help but at the moment I believe I got it.

Answer 9

Ok. The tricky part is applying the chain rule on the (constants) *x * sin (pi*x) part.
There is a definite pattern though. Good luck! :)

Answer 10

I found the third derivative to be -3*pi^2*sin(pi*x) - pi^3*x*cos(pi*x)
and the fourth derivative to be -4*pi^3*cos(pi*x) + pi^4*x*sin(pi*x)
I feel I may have misplaced my signs somewhere but cannot find any particular spot. If I did not mix up my signs somewhere then I need help seeing the pattern for the signs. Will they all be negative past the fourth derivative?

Answer 11

never mind that last sentence was made absolutely no sense I see that now but I still need the help.