Question

find dy/dx and d^2y/dx^2 of x^2+y^2=4. i found dy/dx is = to -2x/2y but can not get the second one right.

Answer 1

try starting off by rewriting it as (-2x)(2y)^-1 ;) and now do it..... see if that helps ;)

Answer 2

reduce
\[\frac{dy}{dx} = -\frac{x}{y}\]
differentiate using quotient rule
\[\frac{dy^{2}}{dx^{2}} = -\frac{y-x \frac{dy}{dx}}{y^{2}} = -\frac{x^{2}+y^{2}}{y^{3}}\]