$derivdef\left(\ln\left(x\right)\right)$

Applicare la formula: $derivdef\left(x\right)$$=\lim_{h\to0}\left(\frac{eval\left(x,var+h\right)-x}{h}\right)$, dove $derivdefx=derivdef\left(\ln\left(x\right)\right)$ e $x=\ln\left(x\right)$

Applicare la formula: $\ln\left(a\right)-\ln\left(b\right)$$=\ln\left(\frac{a}{b}\right)$, dove $a=x+h$ e $b=x$

Applicare la formula: $\frac{a}{b}$$=\frac{1}{b}a$, dove $a=\ln\left(\frac{x+h}{x}\right)$ e $b=h$

Applicare la formula: $a\ln\left(x\right)$$=\ln\left(x^a\right)$, dove $a=\frac{1}{h}$ e $x=\frac{x+h}{x}$

Espandere la frazione $\left(\frac{x+h}{x}\right)$ in $2$ frazioni più semplici con denominatore comune. $x$

Applicare la formula: $\lim_{h\to0}\left(\ln\left(\left(1+\frac{h}{x}\right)^{\frac{1}{h}}\right)\right)$$=\lim_{n\to\infty }\left(\ln\left(\left(1+\frac{1}{n}\right)^{\frac{n}{x}}\right)\right)$, dove $h/x=\frac{h}{x}$, $1+h/x=1+\frac{h}{x}$, $h->0=h\to0$ e $1/h=\frac{1}{h}$

Applicare la formula: $a^{\frac{b}{c}}$$=\left(a^b\right)^{\frac{1}{c}}$, dove $a=1+\frac{1}{n}$, $b=n$, $c=x$ e $b/c=\frac{n}{x}$

Applicare la formula: $\ln\left(x^a\right)$$=a\ln\left(x\right)$, dove $a=\frac{1}{x}$ e $x=\left(1+\frac{1}{n}\right)^n$

Applicare la formula: $\lim_{x\to c}\left(ab\right)$$=a\lim_{x\to c}\left(b\right)$, dove $a=\frac{1}{x}$, $b=\ln\left(\left(1+\frac{1}{n}\right)^n\right)$, $c=\infty $ e $x=n$

Applicare la formula: $\lim_{x\to c}\left(\ln\left(a\right)\right)$$=\ln\left(\lim_{x\to c}\left(a\right)\right)$, dove $a=\left(1+\frac{1}{n}\right)^n$, $c=\infty $ e $x=n$

Applicare la formula: $\lim_{x\to\infty }\left(\left(1+\frac{a}{x}\right)^x\right)$$=e^a$, dove $a=1$ e $x=n$

Applicare la formula: $\ln\left(x\right)$$=logf\left(x,e\right)$, dove $x=e^1$