\triangledown f(x,y) = \left(
\begin{array}{ccc}
y_1a_1 -2b_1\sin\|x\|^2 x_1&\ldots&y_1a_n-2b_1\sin\|x\|^2x_n&\langle a,x\rangle &0&0\\
y_2 a_1 - 2b_2 \sin \|x\|^2 x_1 & \ldots & y_2 a_n - 2b_2\sin \|x\|^2 x_n & 0 & \langle a, x \rangle & 0\\
y_2 a_1 - 2b_2 \sin \|x\|^2 x_1 & \ldots & y_2 a_n - 2b_2\sin \|x\|^2 x_n & 0 & 0 & \langle a, x \rangle \end{array}
\right)