Juan paid $160 for a new lawn mower. A year later, he sold the mower for $136. What is the percent decrease in the value of th
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We first have to find the first derivative before we can find the second. First derivative with respect to x is 
so 
and 
. That's the first derivative. Now for the second it's probably easiest to use the quotient rule, even though it's usually long and drawn out. That looks like this: ![\frac{dy}{dx}= \frac{4y^2(-6x)-[-3x^2(8y \frac{dy}{dx})] }{(4y^2)^2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B4y%5E2%28-6x%29-%5B-3x%5E2%288y%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%5D%20%7D%7B%284y%5E2%29%5E2%7D%20%20)
which simplifies a bit to 
. We will multiply both sides by that denominator to get rid of it which leaves us with 
. Get both dy/dx terms on the same side, and then factor it out. 
. Divide to isolate the dy/dx: 
. There's no simplifying you could do after that that would make any significant difference.