Board 8 > Anagram has more math questions

(+) Yeah! (+)

More specifically, I don't understand how the computer got a result.

Find dy/dx by implicit differentiation.
7radx + rad7 = 9

Now I can easily tell that this becomes (1/2)*7x^(-1/2) + (1/2)y^(-1/2)*y' = 0. All of that is easy and makes perfect sense. My problem is this next part. The computer goes from the result I got to this:

1/radx + y'/7rady = 0

I can see that the x^-1/2 and y^-1/2 are becoming the radicals in the denominators, sure, but the rest is a mystery to me. Where did the 1/2 in both the x and y parts go? How did the 7 get from being in front of the 7 to being in front of the y?
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the right-hand side is zero, so you can multiply the left-hand side by whatever you want and not change it

they multiplied it by 2/7

also the problem as you posed it has no y
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Ah, thank you. That makes sense.
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Got another question.

the speed with which such waves move is given by the expression 2rad(Dr), where r is the reproductive rate of individuals and D is a parameter quantifying dispersal. Calculate v'(r), the derivative of the wave speed with respect to the reproductive rate r.

I can't tell if I'm supposed to use the chain rule or product rule or what. I tried 2(Dr)^1/2 therefore (Dr)^-1/2 therefore 1/radDr, but that's not correct.
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Bump
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because Dr is not the variable. r is the variable. 2rad(Dr) = 2rad(D)rad(r).
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SeabassDebeste posted...

because Dr is not the variable. r is the variable. 2rad(Dr) = 2rad(D)rad(r).

Blehhhh, thanks.
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