>>9615055okay, after some time i finally figured out what the fuck you were asking.
So if im right you should see an explanation for a first order partial derivative. correct? using that equation in that example, you have to use that to find the second order partial derivative.
So you get something like d/dr times (2r dz/dx + 2s dz/dy)
then they apply the product rule to get
2 dz/dx + 2r d/dr(dz/dz)+ 2s d/dr(dz/dy), which should be a highlighted equation for later use in the explanation
now for your question, they use the fucking chain rule again because when you calculate dz/dx, because of the chain rule you have to calculate dx/dr.
So basically in your picture, what you get from those two partial derivatives of dz/dx and dz/dy is what you need to substitute back into the original equation i told you above, which should be equation 5 from your picture.
ALL of this is because you're trying to find the derivative of a composite function of several variables, 2 in your case. So in equation 5, you're just not fully done finding the second partial derivative, you have to calculate further. once you do that, you simplify THEN you have the second order partial derivative.
bitch....
