Question

find the second derivative using implicit differentiation:
9x^2 + y^2 = 9

Answer 1

(9x^2)dy/d + (y^2)dy/d = (9)dy/d
18x + 2y(y') = 0
y' = -18x/2y

Answer 2

or y' = -9/y

Answer 3

9x^2 + y^2 = 9, differentiating to get
18x+2y y '=0,differentiating again to get
18+2[y y ''+y 'y ']=0
[y y ''+y 'y ']=-18/2=-9
[y y ''+(y ')^2]=-9
y y ''=-(y ')^2-9
y ''=(-(y ')^2-9)/y ans....