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Question: for problem 6 i already know how to find the...

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for problem 6, I already know how to find the derivatice of x^n using limit deffinition of derivative. This was required in the last homework set. This one asks for something else. I belive it has something to do with the chain rule as the specific domain of f:(0, inf) must be shown. Please explain each step.  

Exercise 6, Derive a formula for the derivative of f : (0,00) → R given by f(x) = xp, where p E (0, o). Hint: use some of the above exercises.

For problem 8, I have an idea how to solve it. lim x->c [ (f(x))/(g(x))] = lim(f(x)- 0) / (lim g(x) - 0)

= lim(f(x)- c) / (lim g(x) - c) which could easily turn it into f'(c)/g'(c) by definition of limit. However, I do not see how it would make sense to turn c into a 0 here. In your soulution, please state the logic of each step for a thumbs up and write neatly.  

Exercise 8. Let a, be R,a < b. Let f, g : (a, b) → R be differentiable at ce(a, b) with g(c)メ0. Show that L is differentiable at c and establish a formula for , (c).

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