1. The problem statement, all variables and given/known data Question: "Given that the surface x^4 * y^7 + y^6 * z^8 + z^7 * x^9 + 4xyz = 7 has the equation z = f(x,y) in a neighborhood of the point (1,1,1) with f(x,y) differentiable, find the derivatives. Find: a) ∂f/∂x(1,1) b) ∂f/∂y(1,1) c) ∂^2 f/∂x^2" Answers: ∂f/∂x(1,1) = -17/19 = -0.894736842105263 ∂f/∂y(1,1) = -17/19 = -0.894736842105263 ∂^2 f/∂x^2 (1,1) = -2.2399766729844 2. Relevant equations Just taking the derivative of 4x^3 * y^7 + 9x^8 * z^7 + 4yz + ∂f/∂x(8z^7 * y^6 + 7z^6 + 4yz). I also know that ∂f/∂x(1,1) = -17/19. 3. The attempt at a solution I successfully get every single part of this question except the ∂^2 f/∂x^2 part. Instead of isolating for ∂f/∂x and trying to differentiate that again with respect to x (which seems very difficult, if not impossible, to do by hand), I just implicitly differentiate for the second time treating ∂f/∂x as a function. I then just plug in -17/19 for ∂f/∂x(1,1) and plug in the point (1,1,1) and get the wrong answer. I tried computing ∂^2 f/∂x^2 several times and keep getting it wrong so any help would be greatly appreciated. Thanks in advance!