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

1 Answer
Aug 17, 2015

# 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 #