- #1

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"Regard du/dx as the rate of change of u with respect to x, dy/du as the rate of change of y with respect to u, and dy/dx as the rate of change of y with respect to x. If u changes twice as fast as x and y changes three times as fast as u, then it seems reasonable that y changes six times as fast as x, and so we expect that dy/dx = dy/du * du/dx."

I don't understand why it is a simple operation of multiplication to find how fast y changes compared to x. Maybe I am missing something. I'd like to mention, though, that I do understand the chain rule; but when I read this description of it, I just don't seem to understand.