calculus

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

asked by andre
  1. 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

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Find the first partial derivatives and evaluate each at the given point. Function w = 2x^2y − 6xyz + 10yz^2 Point (2, 5, −3) wx(2, 5, −3) = wy(2, 5, −3) = wz(2, 5, −3) =
  2. Calculus

    Find the first partial derivatives and evaluate each at the given point. Function w = sqrt(5x^2 + y^2 − 4z^2) Point (2, −4, 2) wx(2, −4, 2) = wy(2, −4, 2) = wz(2, −4, 2) =
  3. Calculus Partial Derivatives

    y=F(x+at) + f(x-at) y=F(w) + f(v) (w=x+at, v=x-at) don't see how to get from here to partial derivative y with respect to t = F"(w)a^2 + f"(v)a^2
  4. calculus

    find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal
  5. calculus

    a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)
  6. cal3

    Suppose that z=f(x,y) is defined implicitly by an equation of the form F(x,y,z)=0. Find formulas for the partial derivatives ∂f/∂x and ∂f/∂y in terms of F1,F2,F3 To enter your answer use F1, F2, F3 as the partial
  7. Calculus

    Find the four second partial derivatives and evaluate each at the given point. Function f(x, y) = x^3 + 2xy^3 − 9y Point (9, 2) fxx(9, 2) = fxy(9, 2) = fyx(9, 2) = fyy(9, 2) =
  8. Math(Please help)

    Evaluate: f(x,y)=2x^3e^y a) partial derivative with respect to x. I know that you have to treat y as a constant but I have no idea what to do. I do not understand partial derivatives at all. Please help!! b) partial derivative
  9. Math

    ) Suppose that z=f(x,y)z=f(x,y) is defined implicitly by an equation of the form F(x,y,z)=0F(x,y,z)=0. Find formulas for the partial derivatives ∂f∂x∂f∂x and ∂f∂y∂f∂y in terms of F1,F2,F3F1,F2,F3. To enter your
  10. Math(Please help)

    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 especially with the (2,1).

More Similar Questions