Todayʼs the first day Iʼm back at school in quite some time. Iʼve missed around seven days of school; a week and a halfʼs equivalent. Iʼve been doing an enormous amount of math recently, itʼs kept me stimulated. Iʼm trying to explain the chain rule with words at the moment.
! The chain rule comes into play when a function is indirectly dependent on time or the independent. Mathematically: f(g(x)). This can be seen to equal g(x). The objective is to find g(x). Iʼd like to write a graphical proof of this. The overall change of the function (g(x)) is given by the rate of change of the internal function with respect to the independent multiplied by the rate of change of the outside function with respect to the inside function.
! We assume that x, the independent, has varied an increment. For this increment, the function most directly dependent on x will vary, thus causing any functions dependent on it to vary.