(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am confused how the scalar multiple is divided out of the proof of this rule without taking an h with it in the denominator, which would get very tiny meaning the entire thing would go to infinity or negative infinity or zero, you can't tell.

Start with: f(x) = k g(x) End: f'(x) = k g'(x)

2. Relevant equations

This is the proof I was given:

f'(x) = lim(h->0) [k g(x+h) - k g(x)] / h

f'(x) = lim(h->0) [k {g(x+h) - g(x)}] /h

Next step I do not agree with: (Never mind -this is legal, right?)

f'(x) = lim(h->0) k [{g(x+h) - g(x)}/h]

f'(x) = k lim(h->0) [{g(x+h) - g(x)}/h]

f'(x) = k g'(x)

3. The attempt at a solution

This is what I think would happen at the step I disagree with:

f'(x) = lim(h->0) k/h * [{g(x+h) - g(x)}/h]

f'(x) = lim(h->0) k/h * lim(h->0) [{g(x+h) - g(x)}/h]

f'(x) = ??? * g'(x)

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# Homework Help: Proof - the derivative of a scalar multiple

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