Take the derivative of and I'm just confused about where I stop for the first one, how much do I have to simplify. And for the second one, I don't know how to start it. Thanks in advance!
I would leave it like this.
For the second problem, the first thing I would do would be to use the property of logarithms to split this up a bit:
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=
Then
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and then simplify a bit.
The brute force approach also works. It involves the chain rule, the quotient rule, the product rule, and a LOT of cancellations:
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(Sorry. I had to split the second factor up into terms to make the LaTeX work.)
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just like before. (I highly recommend the first method, but the second one is *great* for practice! )
-Dan