Esercizio
$\frac{d}{dx}\left(y\:=\:\left(2x+1\right)^5\left(x^4-3\right)^6\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di equazioni logaritmiche passo dopo passo. d/dx(y=(2x+1)^5(x^4-3)^6). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=y e b=\left(2x+1\right)^5\left(x^4-3\right)^6. Applicare la formula: \frac{d}{dx}\left(x\right)=1. 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(2x+1\right)^5\left(x^4-3\right)^6, a=\left(2x+1\right)^5, b=\left(x^4-3\right)^6 e d/dx?ab=\frac{d}{dx}\left(\left(2x+1\right)^5\left(x^4-3\right)^6\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=5 e x=2x+1.
d/dx(y=(2x+1)^5(x^4-3)^6)
Risposta finale al problema
$y^{\prime}=10\left(2x+1\right)^{4}\left(x^4-3\right)^6+6\cdot 4\left(2x+1\right)^5\left(x^4-3\right)^{5}x^{3}$