$h:R^3 \rightarrow R$ is continuously differentiable and $f:R^3 \rightarrow R$ is defined by $f(u,v,w) = (3u+2v)h(u^2,v^2,uvw)$
Find $D_1 f(u,v,w), D_2 f(u,v,w), D_3 f(u,v,w)$.
So far I have
$D_1 f(u,v,w) = 3(h(u^2,v^2,uvw)) + (3u+2v)(D_1 h(u^2,v^2,uvw)(2u) + D_3h(u^2,v^2,uvw)(vw)) $
$D_2 f(u,v,w) = 2(h(u^2,v^2,uvw)) + (3u+2v)(D_2 h(u^2,v^2,uvw)(2v) + D_3h(u^2,v^2,uvw)(uw)) $
$D_3 f(u,v,w) = (3u+2v)(D_3h(u^2,v^2,uvw)(uv)) $
Is this correct or did I deal with (3u+2v) completely wrong?