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November 26th, 2012, 08:20 PM   #1
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another mind twister

The derV of f(x) = xe^x - e^x


f "(x) = [ xe^x + e^x ] -e^x - book says we got this via the product & Difference Rules


I can't see it; a little help please
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November 26th, 2012, 08:29 PM   #2
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Re: another mind twister

If then:

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November 26th, 2012, 08:42 PM   #3
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Re: another mind twister

Mark

I am trying to apply the product rule.

Would you be so kind to show me the first times the derV of the second + the second times the derV of the first

so that I can see what I am not seeing? It is very embarrassing to keep having the trouble in algebra sometimes I think I have a wet brain or something
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November 26th, 2012, 08:48 PM   #4
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Re: another mind twister

What is where ?
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November 26th, 2012, 08:52 PM   #5
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Re: another mind twister

Not familiar with ER symbols you used on the right, but I do believe that the derV of ke^x is just e^x

the k being constant goes away and in finding the derV of exponential fx's we do the chain rule... so derV of e^x is just e^x and the chain rule would be either 1 or zero gosh I'm reaching hard Mark

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November 26th, 2012, 09:06 PM   #6
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Re: another mind twister

No, the constant doesn't go away, what we have is (and the symbols just mean k is a real constant):



So, when you use this rule along with the product rule, what do you get?
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November 26th, 2012, 09:11 PM   #7
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Re: another mind twister

Hey I don't know if I posted wrong but you have first derV and then 2nd derV;

my post is f(x) and then f '(x).
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November 26th, 2012, 09:53 PM   #8
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Re: another mind twister

Your first post says the derivative is such and such, then the second derivative is...that's what I was going by. But, differentiating a function is the same no matter what we call it.
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November 27th, 2012, 01:30 AM   #9
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The symbol ? means "is in" (in the sense of "is an element of") and is the set of real numbers, so k ? effectively means "k is real". However, k isn't needed for this problem.

Let u = x and v = e^x, so that uv = xe^x. The derivatives of x and e^x are 1 and e^x respectively,
so by the product rule, the derivative of uv = u(dv/dx) + v(du/dx) = x(e^x) + (1)e^x = xe^x + e^x.

Using the above, xe^x - e^x can now be differentiated by the difference rule to give (xe^x + e^x) - e^x.
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November 27th, 2012, 07:58 PM   #10
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Re: another mind twister

Mark,

this is my mistake. It does say this is derV

and then goes on to show the 2nd derV.
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