Final answer:
The question asks to find the expression x(\partial u/\partial x) + y(\partial u/\partial y) for a given function u involving inverse sine. The solution requires applying the chain rule to differentiate u with respect to x and y, and then summing the weighted partial derivatives.
Step-by-step explanation:
The question involves finding the partial derivatives of the function u with respect to x and y, and then combining them in a particular way. The function is given as u = sin-1((x2 + y2) / (x + y)). To find x({partial u} / {partial x}) +
y({partial u} / {partial y}), we need to apply the chain rule to differentiate u with respect to each variable, which can be particularly challenging because u is defined as the inverse sine of a quotient involving both x and y.
First, differentiate u with respect to x, keeping y constant, to get {partial u} / {partial x}. Then, differentiate u with respect to y, keeping x constant, to get {partial u} / {partial y}.
After calculating these derivatives, multiply the first by x and the second by y, and then add the two products to obtain the desired expression.