Risolvere: $\frac{d}{dx}\left(\left(3x-1\right)^2\left(5x+4\right)^6\left(6-4x\right)^5\right)$
Esercizio
$\frac{dy}{dx}\left(3x-1\right)^2\left(5x+4\right)^6\left(6-4x\right)^5$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx((3x-1)^2(5x+4)^6(6-4x)^5). 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=\left(3x-1\right)^2\left(5x+4\right)^6\left(6-4x\right)^5, a=\left(3x-1\right)^2, b=\left(5x+4\right)^6\left(6-4x\right)^5 e d/dx?ab=\frac{d}{dx}\left(\left(3x-1\right)^2\left(5x+4\right)^6\left(6-4x\right)^5\right). 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=\left(5x+4\right)^6\left(6-4x\right)^5, a=\left(5x+4\right)^6, b=\left(6-4x\right)^5 e d/dx?ab=\frac{d}{dx}\left(\left(5x+4\right)^6\left(6-4x\right)^5\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=3x-1. Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=6 e x=5x+4.
d/dx((3x-1)^2(5x+4)^6(6-4x)^5)
Risposta finale al problema
$6\left(3x-1\right)\left(5x+4\right)^6\left(6-4x\right)^5+\left(3x-1\right)^2\left(30\left(5x+4\right)^{5}\left(6-4x\right)^5-20\left(5x+4\right)^6\left(6-4x\right)^{4}\right)$