If u = sin−1[(x + 2y)/(x8 + y8)], then what is the value of x(∂u/∂x) + y(∂u/∂y)?

Explanation

sin u = (x+2y)/(x⁸+y⁸) is homogeneous of degree 1 − 8 = −7. By Euler's theorem on sin u: x·u_x + y·u_y = n·tan u = −7 tan u.