If u = x^2+y^2+z^2 then find the value of x au/ax + y au/ay + z au/az

Question

If u = x^2+y^2+z^2 then find the value of x au/ax + y au/ay + z au/az

Answer 1

u = x² + y² + z²

x(∂u/∂x) + y(∂u/∂y) + z(∂u/∂z) = x(2x) + y(2y) + z(2z) = 2x² + 2y² + 2z² = 2u