> What did they mean by "second"?
They've mentally expanded $$\frac{dJ}{d\alpha}=\int_{x_1}^{x_2}\left(\frac{\partial f}{\partial y}\frac{\partial y}{\partial \alpha}+\frac{\partial f}{\partial \dot{y}}\frac{\partial \dot{y}}{\partial \alpha}\right)\mathrm dx$$ (which I've corrected to be what it says in the image rather than your MathJax) as $$\frac{dJ}{d\alpha}=\int_{x_1}^{x_2}\frac{\partial f}{\partial y}\frac{\partial y}{\partial \alpha} \mathrm dx + \int_{x_1}^{x_2}\frac{\partial f}{\partial \dot{y}}\frac{\partial \dot{y}}{\partial \alpha}\mathrm dx$$
Peter Taylor
·
2021-09-02T11:59:31Z (over 3 years ago)