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April 23rd, 2018, 10:20 PM   #1
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Calculus - Chain Rule

Let f1(x) = e^x, f2(x) = e^f1(x) and generally fn+1(x) = e^fn(x) for all n . For any fixed n, Find the the derivative of fn(x)

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Last edited by arybhatta01; April 23rd, 2018 at 10:22 PM.
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April 23rd, 2018, 11:21 PM   #2
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Hi arybhatta01. Have you made any progress solving this on your own? If so, can you post your work? If not, any thoughts on where to begin?
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April 24th, 2018, 10:14 AM   #3
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You mention the chair rule. If $\displaystyle f_{n+1}(x)= e^{f_n(x)}$, then, using the chain rule, $\displaystyle f_{n+1}'= e^{f_n(x)}(f_n(x)')$. I would be inclined to find the derivatives of the first three or four function, make a "guess" at derivative of the nth function, then try to prove that "guess" using induction.
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Last edited by skipjack; April 24th, 2018 at 07:06 PM.
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April 24th, 2018, 10:53 PM   #4
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Yes . It worked . We need to use chain rule to get the derivative of the 1st 3 function f1 f2,f3 and the use induction to get fn . Thanks.
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