Problems 1F-7bd... Any help?

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Problems 1F-7bd... Any help?

MIT 18.01 Single Variable Calculus (OCW)
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ah.. 1F part 7, b and d....
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yep, part 7, b and d ;)

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okay you there...here we go.
rewrite the fraction taking the square root to the top and write it in exponential form...
|dw:1328639351353:dw|
Now we will use the product rule and chain rule. Remember all terms are constants except for the v's...
|dw:1328639570597:dw|
|dw:1328639645281:dw|
remember m0 is a constant...
that is it for 7b.
give me a minute and i'll look at d.
are you ready for 7 d?
|dw:1328640240270:dw|
I'll use quotient rule this time...
|dw:1328640318517:dw|
|dw:1328640421756:dw|
|dw:1328640527665:dw|
|dw:1328640609299:dw|
|dw:1328640672395:dw|
finished....any questions?
Nope! Thanks a lot again :) Really elucidative. What bothers me is that I can't master this faster way of performing the chain rule, and then I try to name some variables to apply the slow and steady method, which results in further confusion... I'm gonna watch the video lecture again I guess... But I got your method really easily, thanks again!

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