If 5x2 + y4 = −9 then evaluate the second derivative of y with respect to x when x = 2 and y = 1

Question

loser66 · Answer

The easiest way is isolate y

loser66 · Answer

$y = (-5x^2-9)^{1/4}$
then take derivative twice, then apply x=2 in

loser66 · Answer

but if they give you x =2 and y =1, that means they want you to find implicit derivative. ok, just do it

anonymous · Answer

So where would I apply the y? They do want me to find the implicit derivative

loser66 · Answer

do it, just do as usual. 
derivative both sides, right hand side =0, right?
$10x+4y^3y'=0$

loser66 · Answer

hence $y'= \dfrac{-10x}{4y^3}$

loser66 · Answer

let it there, back to the first one, take second derivative

loser66 · Answer

$10 +12y^2y'+4y^3y"=0$

loser66 · Answer

isolate y", you have x, y, y', replace all to get the answer

loser66 · Answer

Next time, if I find out you disappear when I am trying to help you figure out the problem, I will delete my guidance. Please, respect the helpers. We are here for free.