Give a proof for the standard rule of differentiation, the Chain Rule. To do this, use...

Give a proof for the standard rule of differentiation, the Chain Rule. 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 set constructed by intersecting the domain of f with (c,∞), then there is a δ > 0 such that at each point xin the domain of f which lies in (c,c+δ) we have f(x) > f(c). If c is an accumulation point of the domain of f intersected with (−∞, c), then there is a δ > 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 which case you do nothing), and one where g'(x) not= 0 (in which case you use information from 10.1.3).

Expert Solution

Colby Messinger answered 1 year ago

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