calculus
posted by andre
Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.

Steve
x^2+4y^2+16z^2−64 = 0
16z^2 = 64x^24y^2
2z ∂z/∂x = 2x
2z ∂z/dy = 8y
so,
∂z/∂x = x/z
∂z/∂y = 4y/z
∂^2z/∂x^2 = (x^2+z^2)/z^3
and you can do the others similarly, using the quotient rule or the product rule
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