Calcolatrice di Regole di differenziazione di base

1

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

$\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^2$

Applicare la formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$, dove $a=2$ e $x=\frac{x^2+3x+1}{x^2+2x+2}$

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^{2-1}\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

Applicare la formula: $a+b$$=a+b$, dove $a=2$, $b=-1$ e $a+b=2-1$

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^{1}\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

Applicare la formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$, dove $a=2$ e $x=\frac{x^2+3x+1}{x^2+2x+2}$

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^{2-1}\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

Applicare la formula: $a+b$$=a+b$, dove $a=2$, $b=-1$ e $a+b=2-1$

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^{1}\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

2

Applicare la formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$, dove $a=2$ e $x=\frac{x^2+3x+1}{x^2+2x+2}$

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)^{1}\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

3

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

$2\left(\frac{x^2+3x+1}{x^2+2x+2}\right)\frac{d}{dx}\left(\frac{x^2+3x+1}{x^2+2x+2}\right)$

4

Applicare la formula: $\frac{d}{dx}\left(\frac{a}{b}\right)$$=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$, dove $a=x^2+3x+1$ e $b=x^2+2x+2$

$\frac{x^2+3x+1}{x^2+2x+2}\frac{2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^2}$

Applicare la formula: $\frac{a}{b}\frac{c}{f}$$=\frac{ac}{bf}$, dove $a=x^2+3x+1$, $b=x^2+2x+2$, $c=2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)$, $a/b=\frac{x^2+3x+1}{x^2+2x+2}$, $f=\left(x^2+2x+2\right)^2$, $c/f=\frac{2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^2}$ e $a/bc/f=\frac{x^2+3x+1}{x^2+2x+2}\frac{2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^2}$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)\left(x^2+2x+2\right)^2}$

5

Applicare la formula: $\frac{a}{b}\frac{c}{f}$$=\frac{ac}{bf}$, dove $a=x^2+3x+1$, $b=x^2+2x+2$, $c=2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)$, $a/b=\frac{x^2+3x+1}{x^2+2x+2}$, $f=\left(x^2+2x+2\right)^2$, $c/f=\frac{2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^2}$ e $a/bc/f=\frac{x^2+3x+1}{x^2+2x+2}\frac{2\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^2}$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)\left(x^2+2x+2\right)^2}$

Applicare la formula: $x\cdot x^n$$=x^{\left(n+1\right)}$, dove $x^nx=\left(x^2+2x+2\right)\left(x^2+2x+2\right)^2$, $x=x^2+2x+2$, $x^n=\left(x^2+2x+2\right)^2$ e $n=2$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{2+1}}$

Applicare la formula: $a+b$$=a+b$, dove $a=2$, $b=1$ e $a+b=2+1$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

6

Applicare la formula: $x\cdot x^n$$=x^{\left(n+1\right)}$, dove $x^nx=\left(x^2+2x+2\right)\left(x^2+2x+2\right)^2$, $x=x^2+2x+2$, $x^n=\left(x^2+2x+2\right)^2$ e $n=2$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)-\left(x^2+3x+1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

7

Applicare la formula: $-\left(a+b\right)$$=-a-b$, dove $a=x^2$, $b=3x+1$, $-1.0=-1$ e $a+b=x^2+3x+1$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)+\left(-x^2-\left(3x+1\right)\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

8

Applicare la formula: $-\left(a+b\right)$$=-a-b$, dove $a=3x$, $b=1$, $-1.0=-1$ e $a+b=3x+1$

$\frac{2\left(x^2+3x+1\right)\left(\frac{d}{dx}\left(x^2+3x+1\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

Applicare la formula: $\frac{d}{dx}\left(c\right)$$=0$, dove $c=1$

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(3x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

9

La derivata di una somma di due o piÃ¹ funzioni Ã¨ la somma delle derivate di ciascuna funzione.

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(3x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\frac{d}{dx}\left(x^2+2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

Applicare la formula: $\frac{d}{dx}\left(c\right)$$=0$, dove $c=2$

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(3x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(2x\right)\right)\right)}{\left(x^2+2x+2\right)^{3}}$

10

La derivata di una somma di due o piÃ¹ funzioni Ã¨ la somma delle derivate di ciascuna funzione.

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(3x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(2x\right)\right)\right)}{\left(x^2+2x+2\right)^{3}}$

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

$3\frac{d}{dx}\left(x\right)$

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

$3$

11

Applicare la formula: $\frac{d}{dx}\left(nx\right)$$=n\frac{d}{dx}\left(x\right)$, dove $n=3$

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+3\frac{d}{dx}\left(x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(2x\right)\right)\right)}{\left(x^2+2x+2\right)^{3}}$

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

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

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

$2$

12

Applicare la formula: $\frac{d}{dx}\left(nx\right)$$=n\frac{d}{dx}\left(x\right)$, dove $n=2$

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+3\frac{d}{dx}\left(x\right)\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+2\frac{d}{dx}\left(x\right)\right)\right)}{\left(x^2+2x+2\right)^{3}}$

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

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+3\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

13

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

$\frac{2\left(x^2+3x+1\right)\left(\left(\frac{d}{dx}\left(x^2\right)+3\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(\frac{d}{dx}\left(x^2\right)+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

Applicare la formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}$, dove $a=2$

$2x^{\left(2-1\right)}$

Applicare la formula: $a+b$$=a+b$, dove $a=2$, $b=-1$ e $a+b=2-1$

$2x$

14

Applicare la formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}$, dove $a=2$

$\frac{2\left(x^2+3x+1\right)\left(\left(2x+3\right)\left(x^2+2x+2\right)+\left(-x^2-3x-1\right)\left(2x+2\right)\right)}{\left(x^2+2x+2\right)^{3}}$

Calcolatrice di Regole di differenziazione di base

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Calcolatrice di Regole di differenziazione di base

Risolvete i vostri problemi di matematica con la nostra calcolatrice Regole di differenziazione di base passo-passo. Migliorate le vostre abilità matematiche con il nostro ampio elenco di problemi impegnativi. Trova tutte le nostre calcolatrici qui.

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