Give a proof for the standard rule of differentiation, the ChainRule. To do this, use the following information:
10.1.3 Suppose that the function f is differentiable at c, Then,if f′(c) > 0 and if c is an accumulation point of the setconstructed by intersecting the domain of f with (c,∞), then thereis a δ > 0 such that at each point xin the domain of f whichlies in (c,c+δ) we have f(x) > f(c). If c is an accumulationpoint of the domain of f intersected with (−∞, c), then there is aδ > 0 such that at each point y in the domain of f which lies in(c−δ,c) we have f(y) < f(c). (Similar case holds for if f′(c)< 0.)
Create two cases for f'(g(x))*g'(x), one where g'(x)=0 (in whichcase you do nothing), and one where g'(x) not= 0 (in which case youuse information from 10.1.3).
