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    Hey peeps

    Been doing a general cleanup of diff. and got all correct except this little bugger - I keep finding myself going in circles.

    Y = ((xe^x)^2)

    I've been doing...
    step 1; Product rule within the brackets xe^x
    step 2; product rule answer then put into a chain rule

    but then in the chain rule part I have the 'product' rule again (where I have xe^x ).....

    ends up like a product rule, then a chain rule, then a product rule within that chain rule..... yeh I did say circles lol - please help I'm sure its nothing much and more so that I been doing it for 5 hours.

    Been a long day, I hope someone can help show me at what point its going wrong!


    edit; or do I set it to be a chain rule then tackle it as the product rule within that chain rule?
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    Write W = xe^x, so Y = W^2; by the chain rule dY/dx = dY/dW dW/dx
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    No, you want to start with the chain rule. The easiest way to see it is using a substitution:

    y = (xe^x)^2

    Let u = xe^x, then y = u^2

    Now chain rule says that dy/dx = dy/du * du/dx

    What is dy/du? What is du/dx? So what's dy/dx?
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    Ah crickey! thank you

    I've managed to get

     2xe^x  * e^x(1+x)

    Answer is; 2x(1+x)e^2x...

    But, not sure how they simplified the two e^x to e^2x?

    Edit

    Or do they consider e^x to be e^1x in which case it ends up being e^1x * e^1x which is e^2x?
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    Yeah, e^x means e^(1x), giving you e^2x as required.

    Or you can think of it as e^x * e^x = (e^x)^2 = e^2x.
 
 
 
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Updated: March 31, 2011

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