My Math Forum derivative of the function

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 December 4th, 2017, 05:23 PM #11 Senior Member   Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 yes, understood clearly. thanks guys. appreciate Thanks from greg1313
 December 7th, 2017, 03:03 PM #12 Newbie   Joined: Dec 2017 From: USA Posts: 2 Thanks: 0 Hi! I know that this has nothing to do with your questions, yet... I would be tremendously grateful if you could possibly give an answer to my questions and help me with this. I have two questions: first of all, what is the limit of an exponential function as x approaches 0? Is it 1? Second one: how exactly could I calculate lim as h approaches 0 of (1+h/x)^(1/h), that somehow must equal e^(1/x)? I am trying to follow the demonstration of why the derivative of ln is the reciprocal function and one step that is unclear is that limit, that is also written as lim of h as it approaches 0 of (1+h)^(1/xh). I tried to make a conjecture using the binomial formula, but I could not find anything (I am honestly not brave to use it for 1/x as an exponent). The only thing I am aware of is that lim of x as it approaches 0 of (1+x)^(1/x)=e. Thank you very much! Hope you can help me. Fondly, ap calc student.
 December 7th, 2017, 03:13 PM #13 Senior Member     Joined: Sep 2015 From: USA Posts: 2,575 Thanks: 1422 this question should be spun off this thread to it's own
December 7th, 2017, 03:14 PM   #14
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 Originally Posted by adalovelace Hi! I know that this has nothing to do with your questions, yet... I would be tremendously grateful if you could possibly give an answer to my questions and help me with this. I have two questions: first of all, what is the limit of an exponential function as x approaches 0? Is it 1? Second one: how exactly could I calculate lim as h approaches 0 of (1+h/x)^(1/h), that somehow must equal e^(1/x)? I am trying to follow the demonstration of why the derivative of ln is the reciprocal function and one step that is unclear is that limit, that is also written as lim of h as it approaches 0 of (1+h)^(1/xh). I tried to make a conjecture using the binomial formula, but I could not find anything (I am honestly not brave to use it for 1/x as an exponent). The only thing I am aware of is that lim of x as it approaches 0 of (1+x)^(1/x)=e. Thank you very much! Hope you can help me. Fondly, ap calc student.
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