Question

Find f"(x) given that 3x²+y²=2 using implicit differentiation?

Answer 1

`f''(x) = -(3(3x^2+y^2))/y^3`

Explanation:

`3x^2 + y^2 = 2`
Differentiate with respect to `x`:
`6x + 2y(dy)/dx = 0`
Differentiate once more with respect to `x`:
`6 + 2y(d^2y)/dx^2 + 2(dy/dx)^2 = 0`

Re-arrange:
`(d^2y)/dx^2 = -(3(3x^2+y^2))/y^3`