- #1
physics604
- 92
- 2
Homework Statement
Find the second derivative of $$9x^2+y^2=9$$
Homework Equations
Chain rule
The Attempt at a Solution
I find the first derivative first.
$$18x+2y\frac{dy}{dx}=0$$ $$\frac{dy}{dx}=-9\frac{x}{y}$$
I then find the second derivative.
$$-9(\frac{y-x\frac{d'y}{dx''}}{y^2})$$ $$y^2=-9y+9x\frac{d'y}{dx''}$$ $$y^2+9y=9x\frac{d'y}{dx''}$$ $$\frac{d'y}{dx''}=\frac{y^2+9y}{9x}=\frac{y(y+9)}{9x}$$
My textbook says that the answer should be $$\frac{-81}{y^3}$$ What did I do wrong?