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Differentiate xsin(1/x)

How do I differentiate xsin(1/x)

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Product rule. Chain rule. (1/x = x^(-1).)
Reply 2
Avatar for giran
giran
14
^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.
Reply 3
Avatar for s_abbott
s_abbott
OP
5
So I got f'(x)=sin(1/x)-(1/x)cos(1/x)

Is this right at all?
Ciaororwect,
Reply 5
Avatar for fL3X
fL3X
giran
^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.


Brrrrap learnin from TSR
Reply 6
Avatar for DeanK2
DeanK2
giran
^^

Btw, I didn't think you could rewrite 1/x as x^-1 as an angle.


It is a function...
s_abbott
So I got f'(x)=sin(1/x)-(1/x)cos(1/x)

Is this right at all?


Spoiler



What I got...

EDIT: And I got it wrong :h:
Changing it now. :smile:
Reply 8
Avatar for giran
giran
14
Innit man. Safe :smile:
Reply 9
Avatar for Elektrolite
Elektrolite
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
Mathematician!

Spoiler



What I got...


You need to account for the derivative of (1/x) for dv/dx.
Reply 11
Avatar for giran
giran
14
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 :biggrin:

and it'll become -1/x^2 * cos (1/x) when deriving sin(1/x)
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 :huff:
Mathematician!

Spoiler



What I got...

EDIT: And I got it wrong :h:
Changing it now. :smile:

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).
Reply 14
Avatar for s_abbott
s_abbott
OP
5
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??
Reply 15
Avatar for DeanK2
DeanK2
if v = sin(x^-1)

dv/dx = (-x^-2)cos(x^-1)
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. :smile:
Reply 17
Avatar for giran
giran
14
Yes, check my last post.

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

..... I really should learn the latex syntaxing.
Reply 18
Avatar for s_abbott
s_abbott
OP
5
Hahaha cheers guys!!! Take care. Think I'll use TSR more, people are bloody helpful around here
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.

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