Question

If function f(x,y)=cos(x+y); Then what are partial derivatives with respect to x and y i.e., find fx and fy.

Answer 1

To find the partial derivative, say, with respect to x, just differentiate the function as you normally would, but the key thing to remember that everything without x is to be treated as a constant.

For instance, let
g(x,y) = x³y + 2x²y² + ysin(x)
Then the partial derivative of g with respect to x is given by
3x²y + 4xy² + ycos(x)

Answer 2

So here fx and fy are equal right?
fx = fy = -sin(x+y)

Answer 3

Actually, yes, they are equal.