Solución
$$f(tx, ty) = \sqrt{t^2x^2+t^2y^2} = t^1 f(x, y)\\ \frac{\partial f}{\partial y} = x\frac12 \big(x^2+y^2\big)^{-1/2} \times 2x +y\frac12 \big(x^2+y^2\big)^{-1/2} \times 2y = 1 f(x,y)$$