1. Rechenmaschinen
  2. Vorkalkül

Vorkalkül Rechner

Mit unserem Vorkalkül Schritt-für-Schritt-Rechner erhalten Sie detaillierte Lösungen für Ihre mathematischen Probleme. Üben Sie Ihre mathematischen Fähigkeiten und lernen Sie Schritt für Schritt mit unserem Mathe-Löser. Alle unsere Online-Rechner finden Sie hier.

Symbolischer Modus
Text-Modus
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Qui vi mostriamo un esempio di soluzione passo-passo di differenziazione logaritmica. Questa soluzione è stata generata automaticamente dalla nostra calcolatrice intelligente:

$\frac{d}{dx}\left(x^x\right)$
2

Applicare la formula: $\frac{d}{dx}\left(x\right)$$=y=x$, dove $d/dx=\frac{d}{dx}$, $d/dx?x=\frac{d}{dx}\left(x^x\right)$ e $x=x^x$

$y=x^x$
3

Applicare la formula: $y=x$$\to \ln\left(y\right)=\ln\left(x\right)$, dove $x=x^x$

$\ln\left(y\right)=\ln\left(x^x\right)$

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

$\ln\left(y\right)=\ln\left(x^x\right)$

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

$\ln\left(y\right)=x\ln\left(x\right)$
4

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

$\ln\left(y\right)=x\ln\left(x\right)$
5

Applicare la formula: $\ln\left(y\right)=x$$\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right)$, dove $x=x\ln\left(x\right)$

$\frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\ln\left(x\right)\right)$
6

Applicare la formula: $\frac{d}{dx}\left(ab\right)$$=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$, dove $d/dx=\frac{d}{dx}$, $ab=x\ln\left(x\right)$, $a=x$, $b=\ln\left(x\right)$ e $d/dx?ab=\frac{d}{dx}\left(x\ln\left(x\right)\right)$

$\frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right)\ln\left(x\right)+x\frac{d}{dx}\left(\ln\left(x\right)\right)$
7

Applicare la formula: $\frac{d}{dx}\left(x\right)$$=1$

$\frac{d}{dx}\left(\ln\left(y\right)\right)=\ln\left(x\right)+x\frac{d}{dx}\left(\ln\left(x\right)\right)$

Applicare la formula: $\frac{d}{dx}\left(\ln\left(x\right)\right)$$=\frac{1}{x}\frac{d}{dx}\left(x\right)$

$\frac{1}{y}\frac{d}{dx}\left(y\right)=\ln\left(x\right)+x\frac{1}{x}\frac{d}{dx}\left(x\right)$
8

Applicare la formula: $\frac{d}{dx}\left(\ln\left(x\right)\right)$$=\frac{1}{x}\frac{d}{dx}\left(x\right)$

$\frac{1}{y}\frac{d}{dx}\left(y\right)=\ln\left(x\right)+x\frac{1}{x}\frac{d}{dx}\left(x\right)$

Applicare la formula: $\frac{d}{dx}\left(x\right)$$=1$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+x\frac{1}{x}$
9

Applicare la formula: $\frac{d}{dx}\left(x\right)$$=1$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+x\frac{1}{x}$

Applicare la formula: $a\frac{b}{x}$$=\frac{ab}{x}$, dove $a=x$ e $b=1$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+\frac{1x}{x}$

Applicare la formula: $1x$$=x$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+\frac{x}{x}$

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=x$ e $a/a=\frac{x}{x}$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+1$
10

Applicare la formula: $a\frac{b}{x}$$=\frac{ab}{x}$, dove $a=x$ e $b=1$

$\frac{y^{\prime}}{y}=\ln\left(x\right)+1$
11

Applicare la formula: $\frac{a}{b}=c$$\to a=cb$, dove $a=y^{\prime}$, $b=y$ e $c=\ln\left(x\right)+1$

$y^{\prime}=\left(\ln\left(x\right)+1\right)y$
12

Sostituire $y$ con la funzione originale: $x^x$

$y^{\prime}=\left(\ln\left(x\right)+1\right)x^x$
13

La derivata della funzione risulta

$\left(\ln\left(x\right)+1\right)x^x$

Endgültige Antwort auf das Problem

$\left(\ln\left(x\right)+1\right)x^x$

Haben Sie Probleme mit Mathematik?

Detaillierte Schritt-für-Schritt-Lösungen für Tausende von Problemen, die jeden Tag wachsen!