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

2 answers

x^2+4y^2+16z^2−64 = 0
16z^2 = 64-x^2-4y^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
compute the first order partial derivatives of f(x,y) with respect to x and y. assume a constant
Similar Questions
    1. answers icon 0 answers
  1. f(x,y)=x^2 e^2x lny (2,1)I need to find the partial derivatives with respect to x and y. I have not idea how to do this
    1. answers icon 1 answer
  2. find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+yand show that the mixed partial derivatives fxy and
    1. answers icon 0 answers
  3. Evaluate: f(x,y)=2x^3e^ya) partial derivative with respect to x. I know that you have to treat y as a constant but I have no
    1. answers icon 2 answers
more similar questions