Use implicit differentiation to find
∂z/∂x and ∂z/∂y.
x2 + 8y2 + 3z2 = 3
Implicit derivative means that we treat z as a function of x, and we treat y as constant.
We had to multiply because z is treated as a function of x meaning that we have to apply chain rule.
Now, to find we treat z as a function of y and x as a constant.