How do you find $(d^2y)/(dx^2)$ given $x^2+y^2=13$ ?

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Answer 1 · 2016-12-14T15:27:36

See below.

Given $x^2+y^2=13$ ,

$2x+2y dy/dx = 0$ , so

$dy/dx = (-x)/y$ .

Therefore,

$d/dx(dy/dx) = ((-1)y-(-x)dy/dx)/y^2$

$=( -y+x(-x/y))/y^2 * y/y$

$= (-y^2-x^2)/y^3$

$= (-13)/y^3$ .

How do you find (d^2y)/(dx^2)(d^2y)/(dx^2) given x^2+y^2=13x^2+y^2=13?