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# diff. product rule watch

1. Hey peeps

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

I've been doing...
step 1; Product rule within the brackets
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 ).....

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?
2. Write W = xe^x, so Y = W^2; by the chain rule dY/dx = dY/dW dW/dx
3. 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?
4. Ah crickey! thank you

I've managed to get

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?
5. 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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