theo made sails for a model boat.He cut along the diagonal of a rectangular piece of cloth to make two sails as shown below.What
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Differentiate both sides, treating as a function of
. Let's take it one term at a time.
Power, product and chain rules:
Product and chain rules:
Product and chain rules:
The derivative of 0 is, of course, 0. So we have, upon differentiating everything,
Isolate the derivative, and solve for it:
(See comment below; all the 6s should be 2s)
We can simplify this a bit by multiplying the numerator and denominator by to get rid of that fraction in the denominator.