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anonymous
 4 years ago
If x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3)?
anonymous
 4 years ago
If x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3)?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Do you need the answer or explanation?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's for derivatives right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This may go wrong somewhere, but I think this is how it goes: x^2+y^2=25 y^2=x^2+25 y=sqrt(x^2+25)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That's where we start. Now, we need to find the first derivative. We do this by using the formula for the derivatives of composite functions. \[dy/dx=dy/du.du/dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So, y=sqrt(u) u=(x^2+25) y'=1/2(u^1/2) (y' means derivative of y) u'=2x Therefore, dy/dx=1/2(u^1/2)(2x) =x(x^2+25)^1/2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[d ^{2}y / dx ^{2}=(x ^{2}+25)^{1/2}x(1/2)(x ^{2}+25)^{3/2}\]

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.0i get \[d^{2}y/dx = \frac{2x^{2} 25}{\sqrt{25x^{2}}(25x^{2})}\] plug in x=4

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Now, substituting 4 in, we should get the answer. 1/3+2/27 =7/27

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.0is that the same as yours?? i'm off by a neg

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0uhhh, just the negative at the front of my equation is different

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=second+derivative+y%3Dsqrt%2825x%5E2%29+
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