Question

Let d be the distance from a point on the plane x - 2y + 3z = 9 to the point (0, 1, 2). For f(x, y) = d², find the following derivatives.

Answer 1

To find the derivatives of f(x, y) = d², first find the expression for d using the distance formula in 3D space. Then differentiate f(x, y) with respect to x and y to find the derivatives.

Step-by-step explanation:

To find the derivatives of f(x, y) = d², we first need to find the expression for d, which represents the distance from a point on the plane x - 2y + 3z = 9 to the point (0, 1, 2). We can use the distance formula to calculate the distance between two points in 3D space:

d = sqrt((x - 0)² + (y - 1)² + (z - 2)²)

Now, we can differentiate f(x, y) = d² with respect to x and y to find the derivatives:

df/dx = 2d * dd/dx

df/dy = 2d * dd/dy