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hi
I needed some help to solve the following differentiating question.
a) using product rule find
I hope someone can help. Thank you
Regards
ok, lets break it up:
Last edited by luca-deltodesco (2007-04-29 03:20:58)
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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.
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.
Why did the vector cross the road?
It wanted to be normal.
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yes, i did, i often get mixed up when one of the derivitaves is a scalar (fixed)
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thank you thats great guys!
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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Ooh, I didn't know that was true. In that case, yes, definitely do it that way. That's much simpler.
Why did the vector cross the road?
It wanted to be normal.
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A similar question. could you please check if I have worked this out right? Thank you
find dy/dx
I get dy/dx as
im at a loss for how you derived your result...
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even if you expand the brackets before differentiating, you arrive at my same result
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