Question

Differentials!

Answer 1

\[x^3 - y^3 = 1\]

Answer 2

find y'' with respect to x

Answer 3

dy/dx ?

implicit derivative :

3x^2dx - 3y^2dy = 0
x^2dx = y^2dy
dy/dx = x^2/y^2

Answer 4

second derivative :)
the answer is \[\frac{ -2x }{ y^5 }\]

Answer 5

ohh im sorry lol

Answer 6

dy/dx = x^2/y^2
taking the derivative with respect to x:
y'' = (2xy^2-2yy'x^2) / y^4
y'' = (2xy^2-2x^4/y)/y^4
y'' = ( 2xy^3 - 2x^4 )/ y^5

using y^3 = x^3-1
y'' = (2x^4 -2x -2x^4)/y^5
y'' = -2x/y^5