# Natural Logarithm Derivative question

• illu45
In summary, the conversation is about a student who is seeking confirmation on their solution for a homework question involving the derivative of y=ln(ln(ln(x))). They provide their solution and ask for feedback on its correctness.
illu45
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

It looks right to me.

## What is the natural logarithm derivative?

The natural logarithm derivative is a mathematical concept that represents the rate of change of a natural logarithm function at a particular point. It is denoted by the symbol "ln'x" or "d/dx ln(x)".

## How do you find the derivative of a natural logarithm function?

To find the derivative of a natural logarithm function, you can use the formula "d/dx ln(x) = 1/x". This means that the derivative of ln(x) is equal to 1 divided by x.

## What is the significance of the natural logarithm derivative?

The natural logarithm derivative is important in calculus and other areas of mathematics as it helps in finding the slope or rate of change of a natural logarithm function. It is also used in solving various differential equations.

## Is there a difference between the derivative of a natural logarithm and a common logarithm?

Yes, there is a difference between the derivative of a natural logarithm and a common logarithm. The derivative of a natural logarithm is 1/x, whereas the derivative of a common logarithm is 1/(xln10).

## Are there any rules or properties for calculating the natural logarithm derivative?

Yes, there are several rules and properties for calculating the natural logarithm derivative, such as the power rule, product rule, quotient rule, and chain rule. These rules can be used to find the derivative of more complex natural logarithm functions.

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