Lie algebra of $G \times H$.

Question

We have to prove that the Lie algebra of $G \times H$ is $\mathfrak{g}\oplus \mathfrak{h}$.

We know that $\mathfrak{g}=T_eG$ and $\mathfrak{h}=T_eH$. But is it true that $T_e(G\times H)=T_eG\oplus T_eH$?

How to approach this question?

Thanks!