Question

Z=x^3+4x^3y-6xy^2 +y^2 z"=?​

Answer 1

4у-6х+z

вот ответ тадам

Answer 2

To find the second partial derivative of the given function z = x^3 + 4x^3y - 6xy^2 + y^2 with respect to x (z"), we need to take the derivative of the first partial derivative of z with respect to x.

Step 1: Find the first partial derivative of z with respect to x (z'):

z' = ∂z/∂x

To find ∂z/∂x, we differentiate each term of z with respect to x while treating y as a constant:

∂/∂x (x^3 + 4x^3y - 6xy^2 + y^2) = 3x^2 + 12x^2y - 6y^2

Step 2: Now, find the second partial derivative of z with respect to x (z"):

z" = ∂^2z/∂x^2

To find ∂^2z/∂x^2, we differentiate the first partial derivative (z') with respect to x:

∂/∂x (3x^2 + 12x^2y - 6y^2) = 6x + 24xy

So, the second partial derivative of z with respect to x is:

z" = 6x + 24xy