Question

Use the following applet to answer the questions that follow. The given function should be f(x,y)=x²-y². Do not change this function.

Determine ∇f(x,y).

Answer 1

To determine ∇f(x,y), we need to find the partial derivatives of the function f(x,y)=x²-y² with respect to x and y. The gradient vector, denoted by ∇f(x,y), is a vector that contains the partial derivatives of f(x,y) with respect to each variable.

Step-by-step explanation:

To determine ∇f(x,y), we need to find the partial derivatives of the function f(x,y)=x²-y² with respect to x and y. The gradient vector, denoted by ∇f(x,y), is a vector that contains the partial derivatives of f(x,y) with respect to each variable.

Partial derivative with respect to x: ∂f/∂x = 2x

Partial derivative with respect to y: ∂f/∂y = -2y

Therefore, ∇f(x,y) = (2x, -2y).