Natural Logarithm Derivative question

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SUMMARY

The discussion centers on the derivative of the function y=ln(ln(ln(x))). The user, illu45, derived the expression for y' as 1/[ln(ln(x))]*1/[ln(x)]*1/[x]. This derivative calculation is confirmed as correct by another participant in the forum. The conversation highlights the importance of verifying complex derivative calculations in calculus.

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  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the natural logarithm function, ln(x).
  • Knowledge of the chain rule in differentiation.
  • Ability to perform nested function derivatives.
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  • Review the chain rule in calculus for nested functions.
  • Practice calculating derivatives of logarithmic functions.
  • Explore advanced differentiation techniques, such as implicit differentiation.
  • Study the properties of logarithmic functions and their applications in calculus.
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Students studying calculus, particularly those focusing on derivatives, as well as educators seeking to clarify logarithmic differentiation techniques.

illu45
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Hi all,

I'm a bit puzzled by one of my homework questions. I got an answer, but I have nothing to check it with and I'm not sure that my answer is correct.

The question states that y=ln(ln(ln(x))), and asks for y'. This is what I've done, but it seems a bit too simple to me.

y=ln(ln(ln(x)))
y'=1/[ln(ln(x)]*(d/dx)[(ln(ln(x))]
y'=1/[ln(ln(x)]*1/[ln(x)]*(d/dx)[ln(x)]
y'=1/[ln(ln(x)]*1/[ln(x)]*1/[x]

If someone could tell me if the answer is right or wrong (and preferably why its wrong), that'd be very much appreciated.

Thanks,
illu45
 
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