$f(x ,y)$ differentiable all over the plain. $g(u, v) = f(u^2 - v^2, u^2v).$ if $\nabla f (-3, 2) = 2 \vec i + \vec j$ , calculate $ \nabla g(1,2)$ unfortunately, I had to miss the lecture that gradients leant and I don't know how to solve this question.

Let $f(x ,y)$ differentiable all over the plain.
Let $g(u, v) = f(u^2 - v^2, u^2v).$
if $\nabla f (-3, 2) = 2 \vec i + \vec j$ , calculate $ \nabla g(1,2)$
($\vec i$ is unit vector $[1, 0, 0]$ and $\vec j$ is unit vector $[0, 1, 0]$.

I read about gradients, but still don't know how to calculate $\nabla g(1,2).$
Can you please help me solve this question? I'd rather to get help such as hints and general explaination, than a final solution.
Thanks in advance!

$g_u=2uf_u(u^2-v^2,u^2v)+2uvf_v(u^2-v^2,u^2v)$
$g_v=-2vf_u(u^2-v^2,u^2v)+u^2f_v(u^2-v^2,u^2v)$
$g_u(1,2)=2f_u(-3,2)+4f_v(-3,2)=4+4=8$
$g_v(1,2)=-4f_u(-3,2)+f_v(-3,2)=-7$
since $\nabla f(-3,2)=(2,1)$ , means that $f_u(-3,2)=2, f_v(-3,2)=1$
So $\nabla g(1,2)=(g_u(1,2),g_v(1,2))=(8,-7)$
