You are Here: Home >< Maths

# Differentiate xsin(1/x) Watch

1. How do I differentiate xsin(1/x)
2. Product rule. Chain rule. (1/x = x^(-1).)
3. ^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.
4. So I got f'(x)=sin(1/x)-(1/x)cos(1/x)

Is this right at all?
5. Ciaororwect,
6. (Original post by giran)
^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.
Brrrrap learnin from TSR
7. (Original post by giran)
^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.
It is a function...
8. (Original post by s_abbott)
So I got f'(x)=sin(1/x)-(1/x)cos(1/x)

Is this right at all?
Spoiler:
Show

If y = x sin 1/x

u = x, v = sin 1/x
du/dx = 1, dv/dx = -1/(x^2) cos 1/x

u (dv/dx) + v (du/dx) = -1/x cos 1/x + sin 1/x

What I got...

EDIT: And I got it wrong
Changing it now.
9. Innit man. Safe
10. differentiate X, leave sin(1/x) alone. Multiply what you get. Thats 1 *sin(1/x).

then differentiate sin(x^-1) using the chain rule, and leave the X alone. Multiply what you get. So thats X * cos(x^-1) * -X^-2.

Then add the two results of the multiplication. so the end answer is:

1*sin(1/x) + X*cos(x^-1)*-X^-2

Clean it up and your laughing.
Elektrolite
11. (Original post by Mathematician!)
Spoiler:
Show

If y = x sin 1/x

u = x, v = sin 1/x
du/dx = 1, dv/dx = 1/x cos 1/x

u (dv/dx) + v (du/dx) = cos 1/x + sin 1/x

What I got...
You need to account for the derivative of (1/x) for dv/dx.
12. (Original post by DeanK2)
It is a function...
I know, it's just that I've hardly used that rule in exam questions. they give you nice numbers with a constant

and it'll become -1/x^2 * cos (1/x) when deriving sin(1/x)
13. (Original post by Glutamic Acid)
You need to account for the derivative of (1/x) for dv/dx.
Yup, I was correcting it lol. Give me a chance
14. (Original post by Mathematician!)
Spoiler:
Show

If y = x sin 1/x

u = x, v = sin 1/x
du/dx = 1, dv/dx = 1/x cos 1/x

u (dv/dx) + v (du/dx) = cos 1/x + sin 1/x

What I got...

EDIT: And I got it wrong
Changing it now.
you slipped up the dv/dx dude. remember, chain rule. differentiate the whole thing, (cos(1/x)) then times it by the differential of whats in the bracket (-X^-2).
15. Well, I would have got that but I got:
u = x
du/dx = 1

v = sin(1/x)
dv/dx = (-1/x)cos(1/x)

Because 1/x = x^-1 so differentiating that gives -x^-2

Or am I going wrong??
16. if v = sin(x^-1)

dv/dx = (-x^-2)cos(x^-1)
17. (Original post by Glutamic Acid)
You need to account for the derivative of (1/x) for dv/dx.
OK it's now corrected. However the incorrected version is in your quote forever so I can get humiliated by it... FOREVER! NOOOO! Lol.
Ah well, I guess it proves I am human.
18. Yes, check my last post.

dv/dx = -1/(x^2)*cos(1/x)

..... I really should learn the latex syntaxing.
19. Hahaha cheers guys!!! Take care. Think I'll use TSR more, people are bloody helpful around here
20. (Original post by Elektrolite)
you slipped up the dv/dx dude. remember, chain rule. differentiate the whole thing, (cos(1/x)) then times it by the differential of whats in the bracked (-X^-2).
ARGH! Lol I corrected it. Look at my edited version.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 13, 2009
Today on TSR

### Anxious about my Oxford offer

What should I do?

### Am I doomed because I messed up my mocks?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE