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I am reading a proof of the chain rule given in this link: http://kruel.co/math/chainrule.pdf

Here is the portion I am troubled with:

"We know use these equations to rewrite f(g(x+h)). In particular, use the first equation to obtain

f(g(x+h)) = f(g(x) + [g'(x) + v]h),

and use the second equation applied to the right-hand-side with k = [g'(x) + v]h..."

How do they arrive at this, k = [g'(x) + v]h. Based above previous equations and definitions, I don't see how it is possible to write k in terms of the derivative of g(x), v, and h.

Could someone help me?

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# Proof of the Chain Rule

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