Math Help - Differentiable Mappings

1. Differentiable Mappings

I am having trouble solving this question. I know you are supposed to use the limit defnition, but I can't figure it out.

Let F: R^n -> R^m be a differentiable mapping. Given u, v are vectors in R^n, show that
D_(au+bv)F = aD_u(F) + bD_v(F), where a, b: Rn -> R are arbitrary functions.

2. Use that $D_uF(x)=F'(x)u$ where $F'(x)\in\mathbb{R}^{m\times n}$ is the jacobian matrix of $F$ at $x$ .