I was doing my tutorial on Lagrange-Euler formulation for robotic systems when i came across a slight problem. Referring to the picture in the link, I would like to know if my answer (equation 1) (more specifically my method of differentiating) is correct, given that $\theta_1$, $\theta_2$, $\dot{\theta}_1$, and $\dot{\theta}_2$ are all functions of $t$.
Link to picture: http://i48.tinypic.com/5kk5lh.png
Thanks a lot!