A function is given by f(x, y) = y + squareroot 2x - y. Mark the correct option

Question

A function is given by f(x, y) = y + squareroot 2x - y. Mark the correct option in each of the subquestions below. The domain for f consists of all points (x, y) which satisfy x greaterthanorequalto y x greaterthanorequalto 0 og y lessthanorequalto 0 y greaterthanorequalto 2x y notequalto 2x 2x - y lessthanorequalto 1 y greaterthanorequalto 0 The partial derivative f_x (x, y) is equal to 1 + 1/2 squareroot 2x - y 1/2 squareroot 2x - y squareroot 2 1 + 4x 1/squareroot 2x - y 1+y/squareroot 2x - y

Explanation / Answer

a) Domain is all the values of x,y after which the function returns the real values.

For the given function, 2x-y should be greater than 0 for it to be real, so domain condition is 2x>=y

b) partial dervitive with respect to x is (we keep y constant here). Now since the derivative of x^0.5 = 1/2*x^-0.5 therefore the partial derivative of the given function is 1/2*(2x-y)^-0.5*(derivative of (2x-y) = 1/2*(2x-y)^-0.5*2

i.e. = 1/(2x-y)^0.5

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