Esercizio
$\frac{d^4}{dx^4}\left(\frac{1}{3x+2}\right)$
Soluzione passo-passo
Passi intermedi
1
Trovare la derivata ($1$)
$\frac{-3}{\left(3x+2\right)^2}$
Passi intermedi
2
Trovare la derivata ($2$)
$\frac{54x+36}{\left(3x+2\right)^{4}}$
Passi intermedi
3
Trovare la derivata ($3$)
$\frac{54\left(3x+2\right)^{4}-12\left(54x+36\right)\left(3x+2\right)^{3}}{\left(3x+2\right)^{8}}$
Passi intermedi
4
Trovare la derivata ($4$)
$\frac{\left(648\left(3x+2\right)^{3}-12\left(54\left(3x+2\right)^{3}+9\left(54x+36\right)\left(3x+2\right)^{2}\right)\right)\left(3x+2\right)^{8}-24\left(54\left(3x+2\right)^{4}-12\left(54x+36\right)\left(3x+2\right)^{3}\right)\left(3x+2\right)^{7}}{\left(3x+2\right)^{16}}$
Risposta finale al problema
$\frac{\left(648\left(3x+2\right)^{3}-12\left(54\left(3x+2\right)^{3}+9\left(54x+36\right)\left(3x+2\right)^{2}\right)\right)\left(3x+2\right)^{8}-24\left(54\left(3x+2\right)^{4}-12\left(54x+36\right)\left(3x+2\right)^{3}\right)\left(3x+2\right)^{7}}{\left(3x+2\right)^{16}}$