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

1. anonymous

Do you need the answer or explanation?

2. anonymous

d?

3. anonymous

It's for derivatives right?

4. anonymous

This 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)

5. anonymous

That'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. $dy/dx=dy/du.du/dx$

6. anonymous

So, 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

7. anonymous

$d ^{2}y / dx ^{2}=-(-x ^{2}+25)^{-1/2}-x(-1/2)(-x ^{2}+25)^{-3/2}$

8. dumbcow

i get $d^{2}y/dx = \frac{2x^{2} -25}{\sqrt{25-x^{2}}(25-x^{2})}$ plug in x=4

9. anonymous

Now, substituting 4 in, we should get the answer. -1/3+2/27 =-7/27

10. dumbcow

is that the same as yours?? i'm off by a neg

11. anonymous

uhhh, just the negative at the front of my equation is different

12. dumbcow