Calculus: Find the Gradient of the Function at the Given Point

Find the gradient of the function g(x,y) = (x<>2)/2 – (y2)/2 at the point (sqrt(2),1)

Start by taking the partial derivative of the function with respect to x and y

Partial derivative w.r.t. x = x

Partial derivative w.r.t. y = -y

Therefore the Gradient g(x,y) = (x,-y)

Plug the original (x,y) values into the value given by the Gradient g(x,y) to get

Solution: Gradient g(Sqrt(2),1) = (sqrt(2), -1)