Answer
$$ F_{uu\theta} =2\theta v^2\cosh (uv+\theta^2).$$
Work Step by Step
Since $ F(u,v,\theta)=\sinh (uv+\theta^2)$, then using the chain rule, we have
$$ F_{u}=\cosh (uv+\theta^2) (v)=v\cosh (uv+\theta^2),$$
$$ F_{uu}=v\sinh(uv+\theta^2) (v)=v^2\sinh(uv+\theta^2),$$
$$ F_{uu\theta}= v^2\cosh (uv+\theta^2)(2\theta)=2\theta v^2\cosh (uv+\theta^2).$$
