I had a question which reads as follows. A triangle has two of its angular points at $(a,0)$ and $(b,0)$, and the third point $(x,y)$ is movable along $y=x$. If $A$ is an area of the triangle; show that $2(\frac{dA}{dx})=a+b$
While showing the result is no big deal, how do i think about this proposition geometrically? Or rather how do i approach the geometric aspect of these types of 'rates of changes' in general