Question

Given function = xcos(x).

Need to find the general formula for it's derivative when n=n and test it for n=2 or 3.

First five derivatives:-

(f)'= cos(x) - x sin(x)

(f)''=-2 sin(x) - x cos(x)

(f)'''=-3 cos(x) + x sin(x)

(f)''''=4 sin(x) + x cos(x)

(f)'''''=5 cos(x) - x sin(x)

I believe the general formula uses the identity
sin (n * π/2), but I've not been able to find the correct general formula which allows me to plug in values of "n" and get the derivatives of xcos(x)

Answer 1

Any one?

Answer 2

What I know is that the general formula makes use of sin (n * π/2) & cos (n * π/2)

Answer 3

y=xcos(x+n(π/2)), y'=?,y''=?,y'''=?,...

Is that your question?

Answer 4

No. y= xcos(x) is the function

Answer 5

Then what value "n" are you talking about?

Answer 6

I've evaluated the the first five derivatives to find a pattern. Now I need a general formula for the pattern I've found. A general formula which gives me the derivatives of xcos(x)

Answer 7

I see. Alright, give me a sec.

Answer 8

n refers to the number of derivative. For ex. for the first derivative n =1, for the second n=2, etc etc.

Answer 9

I gots dat.

Answer 10

For the nth derivative of the function y=xcos(x), for all n∈ℕ,n>0

(yd^n)/(dx^n)=n(sin(x)d^n)/(dx^n)+x(cos(x)d^n)/(dx^n)

I think that works...

Answer 11

u mean n(derivative of sin(x)^n/derivative of x^n) + x( derivative of cos(x)^n)

Answer 12

Wait a second, let me type this out in LaTeX. XD

Answer 13

lol thnx man

Answer 14

Sorry for taking me a while. XD I was testing my knowledge of LaTeX and failing.

Answer 15

No problem. Lemme check if the equation works. Till then medal awarded ;)

Answer 16

The formula works.. Thnx alot for your help.