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Why do inverse function and chain rule not produce the same derivative?

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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite I understand $'ln(x) = frac1'e^ln(x) =frac1x $ But if I use the chain rule in the denominator to calculate the derivative $'e^ln(x) => ('e^ln(x))('ln(x))=(x)(frac1x)=1$ But then $frac1xneqfrac11$ What am I doing wrong? calculus derivatives share | cite | improve this question asked Sep 4 at 12:36 jhuk 135 8 What is the inverse function of $ln x?$ – gammatester Sep 4 at 12:41 I think your notation might be causing you some confusion. If you write out the statements abstractly with a general function $f$, then carefully substitute your specific function, you should find what you're looking for. This is a good strategy in general. – Prototank Sep 4 at 12:54 add a comment  |  up vote 0 down vote favorite I understand $'ln(x) = frac1'e^ln(x) =frac1x $ But if I use the chain rule in the denominator to c

Hints on solving the equation $3sqrtx-1+sqrt3x+1=2$

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Clash Royale CLAN TAG #URR8PPP up vote 3 down vote favorite 1 I recently stumbled upon the problem $3sqrtx-1+sqrt3x+1=2$, where I am supposed to solve the equation for x. My problem with this equation though, is that I do not know where to start in order to be able to solve it. Could you please give me a hint (or two) on what I should try first in order to solve this equation? Note that I only want hints. Thanks for the help! algebra-precalculus share | cite | improve this question asked Sep 4 at 12:52 ಠ ಠ 990 1 7 34 add a comment  |  up vote 3 down vote favorite 1 I recently stumbled upon the problem $3sqrtx-1+sqrt3x+1=2$, where I am supposed to solve the equation for x. My problem with this equation though, is that I do not know where to start in order to be able to solve it. Could you please give me a hint (or two) on what I should try first in order to solve this equation? Note that I only want hints. Thank