Esercizio
$\frac{d^2}{dx^2}\left(\frac{\left(\cos\:\left(5x^4\right)-1\right)}{x^7}\right)$
Soluzione passo-passo
Passi intermedi
1
Trovare la derivata ($1$)
$\frac{-20x^7x^{3}\sin\left(5x^4\right)-7x^{6}\left(\cos\left(5x^4\right)-1\right)}{x^{14}}$
Passi intermedi
$\frac{-20x^{10}\sin\left(5x^4\right)-7x^{6}\left(\cos\left(5x^4\right)-1\right)}{x^{14}}$
Passi intermedi
3
Trovare la derivata ($2$)
$\frac{x^{14}\left(-20\left(20x^{3}x^{10}\cos\left(5x^4\right)+10x^{9}\sin\left(5x^4\right)\right)-7\left(-20x^{6}x^{3}\sin\left(5x^4\right)+6x^{5}\left(\cos\left(5x^4\right)-1\right)\right)\right)-14x^{13}\left(-20x^{10}\sin\left(5x^4\right)-7x^{6}\left(\cos\left(5x^4\right)-1\right)\right)}{x^{28}}$
Passi intermedi
$\frac{x^{14}\left(-20\left(20x^{13}\cos\left(5x^4\right)+10x^{9}\sin\left(5x^4\right)\right)-7\left(-20x^{9}\sin\left(5x^4\right)+6x^{5}\left(\cos\left(5x^4\right)-1\right)\right)\right)-14x^{13}\left(-20x^{10}\sin\left(5x^4\right)-7x^{6}\left(\cos\left(5x^4\right)-1\right)\right)}{x^{28}}$
Risposta finale al problema
$\frac{x^{14}\left(-20\left(20x^{13}\cos\left(5x^4\right)+10x^{9}\sin\left(5x^4\right)\right)-7\left(-20x^{9}\sin\left(5x^4\right)+6x^{5}\left(\cos\left(5x^4\right)-1\right)\right)\right)-14x^{13}\left(-20x^{10}\sin\left(5x^4\right)-7x^{6}\left(\cos\left(5x^4\right)-1\right)\right)}{x^{28}}$