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#1 2007-04-29 01:03:04

lejoisa
Guest

differentiate

hi

I needed some help to solve the following differentiating question.

a) using product rule find

I hope someone can help. Thank you

Regards

#2 2007-04-29 01:52:14

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: differentiate

ok, lets break it up:

Last edited by luca-deltodesco (2007-04-29 03:20:58)


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#3 2007-04-29 01:54:44

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: differentiate

This one's a bit trickier than normal product rule questions because there are three products in there. You just need to split it up into parts though.

We can use the product rule to find the derivative of xe^2x easily enough.

dx/dx = 1, d(e^2x)/dx = 2e^2x, ∴ d(xe^2x)/dx = (2x+1)e^2x.

Now that we know that derivative, we can find dy/dx.
dy/dx = d(xe^2x)/dx*sin3x + xe^2x*d(sin3x)/dx = (2x+1)e^2xsin3x + 3xe^2xcos3x.

Edit: Ah, Luca beat me. roll
Edit2: But I think he's made a mistake in differentiating xe^2x. It looks like he's differentiated both terms and multiplied them, then added the original thing, instead of adding one original term to the derivative of the other and vice versa.


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#4 2007-04-29 03:20:24

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: differentiate

yes, i did, i often get mixed up when one of the derivitaves is a scalar tongue (fixed)


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#5 2007-04-29 05:05:43

lejoisa
Guest

Re: differentiate

thank you thats great guys!

#6 2007-04-29 20:20:34

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

Re: differentiate

Hi,

You could also make use of the more general product rule, for the case of three functions of x (as you have here) we have:

let y = uvw where each of u,v and w are functions of x then:

The extentsion to n functions of x should be quite obvious.

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#7 2007-04-30 00:12:57

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: differentiate

Ooh, I didn't know that was true. In that case, yes, definitely do it that way. That's much simpler.


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#8 2007-05-01 08:28:30

lejoisa
Guest

Re: differentiate

A similar question. could you please check if I have worked this out right? Thank you

find dy/dx

I get dy/dx as


#9 2007-05-01 08:37:00

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: differentiate

im at a loss for how you derived your result...


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#10 2007-05-01 08:43:41

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: differentiate

even if you expand the brackets before differentiating, you arrive at my same result


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