Natural log

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$y = \sin(x)\,$

$\frac{dy}{dx}=\ ?$

This article/section deals with mathematical concepts appropriate for a student in late high school or early university.

No, this article is not talking about tree, timber or anything wooden.

And no, this article is not talking about Natural law either.

Natural log, a.k.a Natural logarithm, is the logarithm to the base e.
For the real number function, It maps the set of positive real number to the set of real numbers:

$\ln : \mathbb{R}^+ \to \mathbb{R}.$

It's inverse is the exponential function, such that:

$e^{\ln(x)} = x \qquad \mbox{if }x > 0\,\!$

$\ln(e^x) = x.\,\!$

The number e is defined such that

$\frac{d}{dx}\ln(x) = \frac{1}{x}$

Which happens to equal to the following limit:

$e = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n$

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Natural log

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