Exponent properties Calculator
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$\lim_{x\to0}\left(\frac{\ln\left(x+1\right)}{x}\right)$
2
As the limit results in indeterminate form, we can apply L'Hôpital's rule
$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(\ln\left(1+x\right)\right)}{\frac{d}{dx}\left(x\right)}\right)$
3
The derivative of the linear function is equal to $1$
$\lim_{x\to0}\left(\frac{d}{dx}\left(\ln\left(1+x\right)\right)\right)$
4
The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
$\lim_{x\to0}\left(\frac{1}{1+x}\cdot\frac{d}{dx}\left(1+x\right)\right)$
5
The derivative of a sum of two functions is the sum of the derivatives of each function
$\lim_{x\to0}\left(\frac{1}{1+x}\left(\frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)\right)\right)$
6
The derivative of the constant function is equal to zero
$\lim_{x\to0}\left(\frac{1}{1+x}\cdot\frac{d}{dx}\left(x\right)\right)$
7
The derivative of the linear function is equal to $1$
$\lim_{x\to0}\left(\frac{1}{1+x}\right)$
8
Evaluating the limit when $x$ tends to $0$
$\frac{1}{1+0}$